j ourna l ho mepage: www.elsev ier .com/ locate /asoc
uzzy adaptive bacterial foraging congestion management using sensitivityased optimal active power re-scheduling of generators
h Venkaiah ∗, D.M. Vinod Kumarepartment of Electrical Engineering, National Institute of Technology, Warangal (AP), India
r t i c l e i n f o
rticle history:eceived 24 September 2010eceived in revised form 5 April 2011ccepted 2 June 2011vailable online 17 June 2011
a b s t r a c t
This paper presents a new method of fuzzy adaptive bacterial foraging (FABF) based congestion manage-ment (CM) for the first time by optimal rescheduling of active powers of generators selected based onthe generator sensitivity to the congested line. In the proposed method, generators are selected basedon their sensitivity to the congested line to utilize the generators efficiently and optimal rescheduling ofthe active powers of the participating generators was attempted by FABF. The FABF algorithm is tested
on IEEE 30-bus system and Practical Indian 75-bus system and the results are compared with the SimpleBacterial Foraging (SBF) and Particle Swarm Optimization (PSO) algorithms for robustness and effective-ness of congestion management. It is observed from the results that FABF is effectively minimizing thecost of generation in comparison with SBF and PSO for optimal rescheduling of generators to relievecongestion in the transmission line.
BF
. Introduction
A system is said to be congested when the producers andonsumers of electric energy desire to produce and consume inmounts that would cause the transmission system to operate atr beyond one or more transfer limits [1]. The Independent Systemperator’s (ISO) principal challenge in a deregulated environment
s to maintain the power system security and reliability by maxi-izing market efficiency when the system is congested. The ISO
as to create a set of transparent and robust rules that shouldot encourage aggressive entities to exploit congestion to createarket power and maximize their profits at the cost of market. Con-
estion in a transmission system cannot be allowed beyond a shorturation as there is an onset of cascading outages with uncontrolled
oss of load.In the literature survey as detailed in Section 2 of the paper on
arious evolutionary approaches to congestion management, it isbserved that researchers have not attempted so far to dynami-ally adjust the run length vector of the SBF algorithm for optimalescheduling of the active powers of the participating generators bypplying fuzzy criterion to relieve congestion in the congested line.urther, no attempt has been made so far to employ SBF for optimal
escheduling of active power of the select participating generatorso relieve congestion in the congested line. To incorporate the inno-ativeness into congestion management, a new method of FABF
is attempted for the first time to relieve congestion in the con-gested line by optimal rescheduling of active powers of the selectparticipating generators.
Instead of selecting all the generators to relieve congestion, inthis paper it is proposed to select only those generators which arevery sensitive for relieving congestion in transmission lines. Thisis done by the selection of participating generators using genera-tor sensitivities to the power flow on congested lines. Further, itis proposed to solve congestion management problem by optimalrescheduling of active power of participating generators employ-ing the FABF algorithm for the first time. Subsequently, the FABFalgorithm is compared with SBF and conventional PSO algorithmsto determine the best optimal solution for rescheduling the activepower of participating generators to relieve the congestion.
In this paper static congestion management by optimal re-scheduling of active power of the generators selected based ontheir sensitivities to the congested line is attempted by FABF for thefirst time and compared the test results with SBF and conventionalPSO. The main advantage of this approach of relieving congestionin the congested line is quite efficient as it is a non-cost free meanstechnique. This paper illustrates the effectiveness of the proposedmethod on the congestion management problem considering IEEE30-bus system and the Practical Indian 75-bus system.
This paper is organized as follows. Section 2 details the literaturesurvey on various recent evolutionary approaches to congestion
management and Section 3 gives an insight into the proposed FABFalgorithm. Section 4 details the problem formulation of conges-tion management by rescheduling the active power in participatinggenerators selected based on their sensitivities with the congested
ine power flow and the methodology of implementation of FABFlgorithm. The FABF algorithm effectiveness on IEEE 30-bus systemnd Practical Indian 75-bus system is being illustrated in Section 5nd the final outcome of the paper is summed up in Section 6 of theaper as Conclusions.
. Literature survey
R.D. Christie et al. [1] explained in detail the congestion man-gement and felt that controlling the transmission system so thatransfer limits are observed is perhaps the fundamental transmis-ion management problem. In order to relieve congestion, one canither use FACTS devices [2]; operate taps of a transformer, re-ispatch of generation [3] and curtailment of pool loads and/orilateral contracts. In a deregulated environment, all the GENCOsnd DISCOs plan their transactions ahead of time. But by the time ofmplementation of transactions there may be congestion in some ofhe transmission lines. Hence, ISO has to relieve the congestion sohat the system remains in secure state. ISO use mainly two typesf techniques to relieve congestion and they are as follows:
i) Cost free means:a. Out-aging of congested lines.b. Operation of transformer taps/phase shifters.c. Operation of FACTS [2] devices particularly series devices.
i) Non-cost free means:a. Re-dispatch of generation [3] in a manner different from the
natural settling point of the market. Some generators backdown while others increase their output. The effect of this isthat generators no longer operate at equal incremental costs.
b. Curtailment of loads and the exercise of (non-cost-free) loadinterruption options.
R.S. Fang et al. [4] considered an open transmission dispatchnvironment in which pool and bilateral/multi lateral dispatchesoexist and proceeded to develop a congestion management strat-gy for this scenario. K.L. Lo et al. [5] presented congestionanagement techniques applied to various kinds of electricity mar-
ets. Ashwani Kumar et al. [6] reviewed extensively the literatureor reporting several techniques of congestion management andnformed that the congestion management is one of the majorasks performed by Independent System Operators (ISOs) to ensurehe operation of transmission system within operating limits. Inhe emerging electric power markets, the congestion managementecomes extremely important and it can impose a barrier to thelectricity trading. Ashwani Kumar et al. [7] proposed an efficientonal congestion management approach using real and reactiveower rescheduling based on AC Transmission Congestion Distri-ution factors considering optimal allocation of reactive poweresources. The impact of optimal rescheduling of generators andapacitors has been demonstrated in congestion management. H.Y.amina and Shahidehpour [8] described a coordinating mechanismetween generating companies and system operator for congestionanagement using Benders cuts. F. Capitanescu and Van Cutsem [9]
roposed two approaches for a unified management of congestionsue to voltage instability and thermal overload in a deregulatednvironment. J. Fu and Lamont [10] discussed a combined frameork for service identification and congestion management while aew approach were applied to identify the services of reactive sup-ort and real power loss for managing congestion using the upperound cost minimization.
J. Kennedy and Eberhart [11] described the Particle Swarm Opti-ization (PSO) concept in terms of its precursors, briefly reviewing
he stages of its development from social simulation to optimizernd discussed application of the algorithm to the training of artifi-
ft Computing 11 (2011) 4921–4930
cial neural network weights. Y. Shi [12] surveyed the research anddevelopment of PSO in five categories viz. algorithms, topology,parameters, hybrid PSO algorithms and applications. In general, thesearch process of a PSO algorithm should be a process consisted ofboth contraction and expansion so that it could have the ability toescape from local minima, and eventually find good enough solu-tions. Y. del Valle et al. [13] presented a detailed review of the PSOtechnique, the basic concepts and different structures and variants,as well as its applications to power system optimization problems.Z.X. Chen et al. [14] introduced PSO for solving Optimal PowerFlow (OPF) with which congestion management in pool market ispractically implemented on IEEE 30 Bus system and proved thatcongestion relief using PSO is effective in comparison with InteriorPoint Method and Genetic Algorithm approach. J. Hazra and Sinha[15] proposed cost efficient generation rescheduling and/or loadshedding approach for congestion management in transmissiongrids using Multi Objective Particle Swarm Optimization (MOPSO)method. S. Dutta and Singh [3] proposed a technique for reducingthe number of participating generators and optimum reschedulingof their outputs while managing congestion in a pool at minimumrescheduling cost and explored the ability of PSO technique insolving congestion management problem. D.M. Vinod Kumar andVenkaiah [2] obtained an optimal solution for static congestionmanagement using PSO based OPF method. Here, the congestionhas been created in the transmission line by loading the lines andit is relieved by placing a Static Synchronous Series Compensator(SSSC) in an optimal location in the transmission line. D.N. Jeyaku-mar et al. [16] demonstrated the successful adaptation of the PSOalgorithm to solve various types of economic dispatch (ED) prob-lems in power systems viz. Multi-area ED with tie line limits, EDwith multiple fuel options, combined environmental ED and EDof generators with prohibited operating zones. The better compu-tation efficiency and convergence property of the PSO techniqueshows that it can be applied to a wide range of optimization prob-lems. Z.-L. Gaing [17] proposed a PSO method for solving the EDproblem with the generator constraints and demonstrated that thePSO method can avoid the shortcoming of premature convergenceof Genetic Algorithm (GA) method while obtaining higher qual-ity solution with better computation efficiency and convergenceproperty.
K.M. Passino [18] explained in detail the biology and physicsunderlying the chemotactic (foraging) behavior of Escherichia colibacteria that formulated Simple Bacterial Foraging (SBF) Optimiza-tion Algorithm for optimization process represented by the activityof social bacterial foraging. The algorithm presented in [18] hasbeen utilized in this paper for optimal generation of active powerof the participating generators. The SBF algorithm along with theprocedure to create fuzzy logic rules using fuzzy toolbox of MAT-LAB 7.01 package to fuzzify the run length vector C(i) for optimalvalue is incorporated in Appendix A of this paper for easy ref-erence and the pseudo code of modified algorithm viz. FABF isdetailed in Section 3 for solving the optimization problem. Janar-dan Nanda et al. [19] made a maiden attempt to examine andhighlight the effective application of Bacterial Foraging algorithmto optimize several important parameters in Multiarea AutomaticGeneration Control (AGC) of a thermal system and compared itsperformance to establish its superiority over Genetic Algorithm(GA) & classical methods. B.K. Panigrahi and V Ravikumar Pandi[20] presented a novel stochastic optimization approach to solveconstrained economic load dispatch problem using hybrid bacterialforaging technique. M. Tripathy et al. [21] observed that simulta-neous tuning of the UPFC lead-lag type controller parameters with
the bacterial foraging algorithm gave robust damping performancewith variable operating conditions and severity of faults. It is con-cluded that the bacterial foraging algorithm is quite efficient insolving highly nonlinear optimization problems. B.K. Panigrahi and
lied So
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C. Venkaiah, D.M. Vinod Kumar / App
Ravikumar Pandi [22] presented the effective implementationf Adaptive Bacterial Foraging – Nelder–Mead (ABFNM) algorithmor removing the congestion in the transmission line by generatorescheduling of all the generators in the test system by optimiz-ng the cost involved in the rescheduling process. Here, the ABFNMlgorithm is not utilized for reduced generators participation ofhe test system to relieve congestion. Further, if the test systemize is large, the optimal rescheduling of all the generators in theest system is quite tedious and the computational complexityrows with the test systems size for relieving the congestion. H.upriyono and M.O. Tokhi [24] presented the development of a newpproach involving adaptable chemotactic step size in bacterial for-ging algorithm. Test results with bench mark functions show thatBF with the proposed adaptable chemotactic step size mechanisms able to converge faster to the global optimum than the standardBF. N. Sinha et al. [25] developed an algorithm based on hybridiza-ion of SBF and Differential Evolution (DE) to solve the problem ofnding the optimum load allocation among the committed units in
power system with non-convex loads. Results demonstrate thathe performance of the hybrid algorithm is much better than SBFn terms of convergence rate and solution quality. H. Vahedi et al.26] proposed a novel Mixed Integer SBF algorithm for solving con-trained OPF problem for practical applications. Results show thathe Mixed Integer SBF algorithm is superior to PSO based algorithmn terms of solution quality, convergence rate and evolutionaryomputing time.
The survival of species in any natural evolutionary processepends upon their fitness criteria, which relies upon their foodearching and motile behavior. The law of evolution supports thosepecies who have better food searching ability and either elimi-ates or reshapes those with poor search ability. The genes of thosepecies who are stronger get propagated in the evolution chainince they possess ability to reproduce even better species in futureenerations. So, a clear understanding and modeling of foragingehavior in any of the evolutionary species, leads to its suitablepplication in any non-linear system optimization algorithm. Theoraging strategy of E. coli bacteria present in the human intestinean be explained by four processes namely Chemotaxis, Swarming,eproduction, and Elimination & Dispersal.
Chemotaxis: The characteristics of movement of bacteria inearch of food can be defined in two ways, i.e. swimming and tum-ling together known as chemotaxis. A bacterium is said to bewimming if it moves in a predefined direction, and tumbling ifoving in an altogether different direction. Mathematically, tum-
le of any bacterium can be represented by a unit length of randomirection �(i) multiplied by a step length of that bacterium C(i). Inase of swimming this random length is predefined.
There is a scope to fuzzify the variable C(i) for arriving at theptimum value of the step size for the given problem in less time.nitially the run length vector C(i) value is selected by random selec-ion and it plays an important role in the convergence of SBF [18]lgorithm. A small value of C(i) causes slow convergence, whereas
large value may fail to locate the minima by swimming throughhem without stopping. The selection of C(i) is tedious and timeonsuming in SBF. Hence, fuzzy adaptive scheme is utilized to C(i)or ensuring the convergence of SBF algorithm. Here, the fuzzynput variables are taken as C(i) and the error from the objectiveunction to obtain the fuzzy output as �C(i) for optimal value. The
uzzy toolbox of MATLAB 7.01 package on Windows environments employed to fuzzify the run length vector C(i) and the procedureo create fuzzy logic rules using fuzzy logic toolbox is detailed inppendix A.
ft Computing 11 (2011) 4921–4930 4923
Swarming: For the bacteria to reach at the richest food location(i.e. for the algorithm to converge at the solution point), it is desiredthat the optimum bacterium till a point of time in the search periodshould try to attract other bacteria so that together they convergeat the solution point more rapidly. To achieve this, a penalty func-tion based upon the relative distances of each bacterium from thefittest bacterium till that search duration, is added to the originalcost function. Finally, when all the bacteria have merged into thesolution point this penalty function becomes zero. The effect ofswarming is to make the bacteria congregate into groups and moveas concentric patterns with high bacterial density.
Reproduction: The original set of bacteria, after getting evolvedthrough several chemotactic stages reach the reproduction stage.Here, the best set of bacteria (chosen out of all the chemotacticstages) gets divided into two groups. The healthier half replaces theother half of bacteria, which gets eliminated, owing to their poorerforaging abilities. This makes the population of bacteria constantin the evolution process. The survival and elimination behavior ofany bacterium is better known as its motile behavior.
Elimination and dispersal: In the evolution process a suddenunforeseen event can occur, which may drastically alter the smoothprocess of evolution and cause the elimination of the set of bacte-ria and/or disperse them to a new environment. Most ironically,instead of disturbing the usual chemotactic growth of the set ofbacteria, this unknown event may place a newer set of bacterianearer to the food location. From a broad perspective, eliminationand dispersal are parts of the population level long distance motilebehavior. In its application to optimization it helps in reducing thebehavior of stagnation (i.e. being trapped in a premature solutionpoint or local optima) often seen in such parallel search algorithms.
The proposed FABF algorithm for optimal rescheduling of par-ticipating generators active power for relieving congestion in thetransmission line on the two test systems is explained in detail inAppendix A.
The pseudo-code of the proposed FABF algorithm for congestionmanagement by optimal rescheduling of participating generatorsis as follows:
1. Initialize parameters p, S, Ns , Nc , Nre , Ned , Ped , C(i) (i = 1,2, . . ., S), �i .2. Elimination-dispersal loop: l = l + 13. Reproduction loop: k = k + 14. Chemotaxis loop: j = j + 1
[a] For i = 1,2, . . ., S //take a chemotactic step for bacteriumi
Else, m = Ns //End of while statement[h] Go to next bacterium (i + 1) if
/= S//Go to [b] to process the nextbacterium
. If j < Nc , Go to 4 //to continue chemotaxis, since the lifeof the bacteria is not over
. Reproduction:For the given k and l, and for each
= 1,2, . . ., S,
Jihealth
=Nc+1∑j=1
Jerror (i, j, k, l)
If k < Nre , Go to 3 //to perform reproduction. Elimination-dispersal:For i = 1,2, . . ., S, with probability ped ,Perform elimination dispersal //to eliminate and disperse one to a
random locationIf l < Ned , Go to 2 Otherwise end
The flow chart of the proposed FABF algorithm is shown in Fig. 1.
. Problem formulation
In a power system, the economic operation of generating utili-ies is always preferred. In the deregulated market environment therst part of the power dispatch problem is to find out the preferredchedule using Optimal Power Flow (OPF) and the second part isescheduling the generation for removing the congestion. The OPFroblem is about minimizing the fuel cost of generating units for
specific period of operation so as to accomplish optimal gener-tion dispatch among operating units and in return satisfying theystem load demand, generator operation constraints and line flowimits. The objective function of the OPF problem [22] as illustratedn Appendix B of this paper is utilized for formulating the opti-
ization problem to have efficient solution in solving congestionanagement.The generators in the system under consideration have different
ensitivities to the power flow on the congested line. A change ineal power flow in a transmission line k connected between bus ind bus j due to change in power generation by generator g can beermed as generator sensitivity to congested line (GS). Mathemat-cally, GS for line k can be written as
Sg = �Pij
�Pg(1)
here Pij is the real power flow on the congested line k and Pg ishe real power generated by generator g.
It is advisable to select the generators having non uniform andarge magnitudes of sensitivity values as the ones most sensitive tohe power flow on the congested line and to participate in conges-ion management by rescheduling their power outputs. Based onhe bids received from the participant generators, the amount ofescheduling required is computed by solving the following opti-ization problem.
C = minimize
Ng∑g
Cg(�Pg) �Pg (2)
ubject to
Ng∑g=1
((GSg) �Pg) + PF0k ≤ PFmax
k , k = 1, 2, 3, . . . , Nl (3)
Pming ≤ �Pg ≤ �Pmax
g (4)
Pming = Pg − Pmin
g (5)
Pmaxg = Pmax
g − Pg, where g = 1, 2, 3, . . . , Ng (6)
ft Computing 11 (2011) 4921–4930
Ng∑g=1
�Pg = 0 (7)
where �Pg is the real power adjustment at bus-g and Cg(�Pg) arethe incremental and decremented price bids submitted by gener-ators and these generators are willing to adjust their real poweroutputs. PF0
kis the power flow caused by all contracts requesting
the transmission service. PFmaxk
is the line flow limit of the lineconnecting bus-i and bus-j. Ng is the number of participating gen-erators, Nl is the number of transmission lines in the system, Pmin
gand Pmax
g denote respectively the minimum and maximum limitsof generator outputs. It can be seen that the power flow solutionsare not required during the process of optimization.
The parameters selected for the proposed FABF algorithm is asfollows:
Number of bacteria, S = 20.Number of chemotactic steps, Nc = 30.Swimming length, Ns = 4.Number of reproduction steps, Nre = 10.Number of elimination & dispersal events, Ned = 5.Run length vector initial value, C(i) = 0.05.Probability of elimination & dispersal, Ped = 0.02.Number of bacteria reproduction, Sr = S/2.Fuzzy rules = 56.
The parameters selected for SBF algorithm are same as thoseof FABF excepting the fuzzy rules. The parameters selected for theconventional PSO are as follows:
The IEEE 30-bus system consists of six generator busesand 24 load buses. The network topology and the test datafor the IEEE 30-bus system can be found in http://www.ee.washington.edu/research/pstca. In this system congestion is cre-ated by loading incrementally at load Bus-14 in steps of small unitstill some line crosses its thermal limit. Congestion occurred in Line-26 connecting Bus-10 and Bus-17 when the system is loaded atload Bus-14. The unconstrained scheduled power flow of 7.01 MWis recorded in Line-26 whose power flow limit is 6.99 MW. Hence,Congestion has to be relieved by optimal rescheduling of the activepower generation of the generators. Accordingly, the GeneratorSensitivities are computed for the congested Line-26 using Eq. (1)for the system, shown in Fig. 2. Generators which are to partici-pate in congestion management are to be selected depending ontheir sensitivities to the congested line. In this test system, it isobserved that all the generators show strong influence on the con-gested line. This is perhaps the system is very small and generallyvery tightly connected electrically. All the generators are participat-ing in congestion management and the evolutionary algorithms areemployed to optimally reschedule the active power of the genera-tors for relieving congestion in Line-26.
Table 1 gives the active power generation by the six participat-
ing generators before the congestion management and after thecongestion management employing FABF, SBF and PSO.
The rescheduling of active power of the participating generatorsby FABF, SBF and PSO is pictorially shown in Fig. 3 for comparison
Initialize all va riables. Set all loop counters and bacterium index i
equal to 0
Increase elimination dispersion loop counter
l=l+1
Increase Chemotactic loop counter
j=j+1
Perform Elimination dispersal (For i=1,2,…S with probability Ped, eliminate and disperse one
to a random location)
Perform Reproduction (by killing the worse half
of the population w ith higher cumulative health and splitting the better
half into two
Increase Reproduction loo p counterk = k + 1
K < Nre?
J < N? c
l < Ned?
Increase bacterium index i=i+1
Compute the objective function value for the ith bacterium as Jerror(i,j,k,l) adding the
cell to cell attractant effect to nutrient concentration and set Jlast= Jerror(i,j,k,l)
Tumble (Let the ith bacterium take a step of heignt C(i ) along a randomly generate d
tumble vector Δ(i)) Fuzzify C(i)
Compute the objective function value Jerror(i,j+1,k,l) taking into account the cell -
to-cell attractant effect
Set Swim Counterm = 0
m = m + 1 Set m = Ns
Jerror(i,j+1,k,l) < Jlast?
m < Ns?
i < S? Set Jlast= Jerror(i,j+1,k,l) Swim (Let the ith bacterium take a step of height C(i) along the direction of the same
tumble vector Δ(i))
Start
Yes
No
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
ptive
wm
7o
Fig. 1. Flow chart of fuzzy ada
ith active power generation before and after congestion manage-
ent.Table 2 shows the unconstrained scheduled power flow of
.01 MW in the congested Line-26 connecting Bus-10 and Bus-17f IEEE 30-bus system whose line flow limit is 6.99 MW before con-
bacterial foraging algorithm.
gestion management and the power flow in the congested line after
relieving congestion by FABF, SBF and PSO algorithms.
The line flow in congested line after relieving the congestionusing FABF, SBF and PSO algorithms is pictorially shown in Fig. 4 incomparison with unconstrained scheduled power flow.
Fig. 2. Generator sensitivity factors of Line 26 for IEEE 30-bus system.
0
50
100
150
200
250
13118521
Ac�
ve P
ower
Gen
era�
on (M
W)
Generator Buses
FABF(BCM)
FABF(ACM)
SBF(BCM)
SBF(ACM)
PSO(BCM)
PSO(ACM)
Fig. 3. Active power generation of each selected generator for congestion manage-ment in IEEE 30-bus system (BCM = before congestion management; ACM = aftercongestion management).
Table 2Active power flow in the congested line before and after congestion managementfor IEEE 30-bus system.
Branch power flow Before congestionmanagement activepower flow (MW)
After congestionmanagement activepower flow (MW)
From bus To bus FABF SBF [18] PSO [3]
10 17 7.01 6.78 6.98 6.9
6.65
6.7
6.75
6.8
6.85
6.9
6.95
7
7.05
Before CM FABF a�er CM SBF a�er CM PSO a�er CM
Ac�
ve P
ower
Flo
w (M
W) i
n Li
ne 2
6
Fig. 4. Active power flow in Line 26 (Bus-10 to Bus-17) for IEEE 30-bus System.
Table 3Comparisons of cost of congestion management (CM) for IEEE 30-bus system.
Cost of CM (Rs/MWh) FABF SBF [18] PSO [3]
Best 149.96 177.12 160.23Mean 150.38 177.36 161.49Worst 150.42 177.38 161.61
The evolutionary algorithms have been implemented for twelvetimes on the IEEE 30-bus system to know the robustness and effec-tiveness of the proposed method. Table 3 shows best value, worstvalue and mean value after the congestion management for optimalrescheduling of the active powers of the participating generators.
The pictorial representation of cost of congestion managementutilizing FABF, SBF and PSO is shown in Fig. 5. It is observed fromFig. 5 that FABF algorithm gives minimum cost for rescheduling ofactive power of participating generators to relieve congestion. It isfurther observed that the time taken for the best run among the 12runs of evolutionary algorithms for congestion management is lessin the case of FABF.
The comparison of convergence characteristics of FABF, SBF andPSO algorithms on IEEE 30-bus system in Fig. 6 reveals that FABFis quite faster in optimization leading to reduction in computationburden.
5.2. Case B: practical Indian 75-bus system
The Practical Indian 75-bus system consists of fifteen genera-tor buses and 60 load buses. The single line diagram of the testsystem along with the characteristics of the generating units andtheir constraints are available in [23]. In this test system congestionis created by loading Bus-57 in steps of small units till some linecrosses its thermal limit. Congestion occurred in Line-46 connect-ing Bus-30 and Bus-57 when the system is loaded at Bus 57. Theunconstrained scheduled power flow of 191.45 MW is recorded inLine-46 whose power flow limit is 191.23 MW. Hence, Congestion
has to be relieved by rescheduling the active power generation ofthe participating generators. Accordingly, the Generator Sensitiv-ities are computed for the congested Line-46 using Eq. (1) for thesystem and they are plotted in Fig. 7. Generators which are to par-
135
140
145
150
155
160
165
170
175
180
PSOSBFFABF
Cost
of G
ener
a�on
in R
s./M
Wh
Conges�on Management Methods
Best (Rs./MWh))
Mean(Rs./MWh)
Worst(Rs./MWh)
Fig. 5. Comparison of cost of generation for IEEE 30-bus system.
Fig. 8. Active power generation of each selected generator for congestion manage-ment in Indian 75-bus system (BCM = before congestion management; ACM = aftercongestion management).
Table 5Active power flow in the congested line before and after congestion managementin Indian 75-bus system.
Branch power flow Before congestionmanagement activepower flow (MW)
After congestionmanagement activepower flow in MW
effectiveness of the proposed method. Table 6 shows best value,worst value and mean value after the congestion management foroptimal rescheduling of the active powers of the participating gen-
ig. 6. Plot of convergence of the algorithms with cost function on IEEE 30 Busystem.
icipate in congestion management are to be selected dependingn their sensitivities to the congested line. In this test system, its observed that only six generators show strong influence on theongested line and so these six generators are selected for conges-ion management. The evolutionary algorithms are employed toptimally reschedule the active power of the selected generatorsor relieving congestion in Line-46.
Table 4 gives the active power generation by the six participat-ng generators before the congestion management and after theongestion management employing FABF, SBF and PSO.
The rescheduling of active power of the participating generatorsy FABF, SBF and PSO for relieving congestion is pictorially shown
n Fig. 8 for comparison with active power generation before andfter congestion management.
Table 5 shows the unconstrained scheduled power flow of91.45 MW in the congested Line-46 connecting Bus-30 and Bus-7 of Practical Indian 75-bus system whose line flow limit is
00.5
11.5
22.5
33.5
44.5
5
151413121110987654321
Gen
erat
or S
ensi
�vi
ty
Generator Buses
Indian 75 -Bus System
ig. 7. Generator sensitivity factors of Line 46 for Practical Indian 75-bus system.
From bus To bus FABF SBF [18] PSO [3]
30 57 191.45 188.89 190.23 190.012
191.23 MW before congestion management and the power flow inthe congested line after relieving congestion utilizing FABF, SBF andPSO algorithms.
The line flow in congested line after relieving the congestionusing FABF, SBF and PSO algorithms is pictorially shown in Fig. 9 incomparison with unconstrained scheduled power flow.
The evolutionary algorithms have been implemented for twelvetimes on the Practical Indian 75-bus system for robustness and
erators.
187.5
188
188.5
189
189.5
190
190.5
191
191.5
192
Before CM FABF a�er CM SBF a�er CM PSO a�er CM
Ac�
ve P
ower
Flo
w (M
W) i
n Li
ne-4
6
Fig. 9. Active power flow in Line-46 (Bus-30 to Bus-57) of Practical Indian 75-busSystem.
4928 C. Venkaiah, D.M. Vinod Kumar / Applied So
Table 6Comparisons of cost of congestion management (CM) for Practical Indian 75-bussystem.
Cost of CM (Rs/MWh) FABF SBF [18] PSO [3]
Best 236.25 255.45 240.64Mean 238.16 256.24 241.32Worst 238.33 256.31 241.38
225
230
235
240
245
250
255
260
PSOSBFFABF
Cost
of G
ener
a�on
inRs
./M
Wh
Conges�on Management Methods
Best (Rs./MWh)
Mean(Rs./MWh)
Worst (Rs./MWh)
Fig. 10. Comparison of cost of generation for Practical Indian 75-bus system.
F7
uFoi1l
Ptc
t
TC
ig. 11. Plot of convergence of the algorithms with cost function on Practical Indian5 Bus System.
The pictorial representation of cost of congestion managementtilizing FABF, SBF and PSO is shown in Fig. 10. It is observed fromig. 10 that FABF algorithm gives minimum cost for reschedulingf active power of participating generators to relieve congestion. Its further observed that the time taken for the best run among the2 runs of evolutionary algorithms for congestion management is
ess in the case of FABF.The comparison of convergence characteristics of FABF, SBF and
SO algorithms on Practical Indian 75-bus system in Fig. 11 reveals
hat FABF is quite faster in optimization leading to reduction inomputation burden.
It is found from Table 7 that the FABF algorithm took very lessime to relieve congestion by optimal rescheduling of active powers
able 7omparison of CPU time (in seconds).
Test system FABF SBF [18] PSO [3]
IEEE 30-bus system 4.125 6.23 11.256Indian 75-bus system 6.85 15.23 18.851
ft Computing 11 (2011) 4921–4930
of participating generators in both the test systems. The simula-tion was carried out on Pentium® 4 CPU, 3.00 GHZ 496 MB of RAMPersonal Computer.
6. Conclusion
In this paper congestion management problem has been solvedusing optimal rescheduling of active powers of generators selectedbased on the generator sensitivity to the congested line, utilizingfuzzy adaptive bacterial foraging (FABF) algorithm for the first time.Here rescheduling is done taking into consideration the minimiza-tion of cost and satisfying line flow limits. The results obtainedby the fuzzy adaptive bacterial foraging (FABF) are compared withSimple Bacterial Foraging (SBF) and conventional PSO algorithms.All these three methods are tested on IEEE 30-bus and PracticalIndian 75-bus systems. In the case of Indian 75-bus system onlysix generators out of fifteen generators are selected based on thegenerator sensitivities to the congested line for relieving conges-tion in the congested line, thereby reducing the generator costs.The results show that fuzzy adaptive bacterial foraging (FABF)algorithm is giving the best optimal solution in comparison withSimple Bacterial Foraging (SBF) and conventional PSO algorithmswith respect to cost and runtime for relieving congestion in thecongested line.
Appendix A. FABF algorithm for congestion managementby optimal rescheduling of generators
The proposed FABF algorithm [18] for congestion managementby optimal rescheduling of participating generators is as follows:
Step 1. Initialization:a) Number of parameters (p) to be optimized.b) Number of bacteria (S) to be used for searching the total region.c) Swimming length Ns after which tumbling of bacteria will be
undertaken in a chemotactic loop.d) Nc, Number of iterations to be undertaken in a chemotactic loop
(Nc > Ns).e) Nre, the maximum number of reproduction to be undertaken.f) Ned, the maximum number of elimination and dispersal events
to be imposed over bacteria.g) Ped, the probability with which the elimination and dispersal
will continue.h) The position of each bacterium P(j, k, l) = {�i(j, k, l)|i = 1, 2, . . .,
S} at the jth chemotactic step, kth reproduction step, and lthelimination-dispersal event.
i) The value of C(i) > 0, where i = 1,2, . . . S denotes a basic chemo-tactic step size.
j) The values of dattract, wattract, hrepellant, and wrepellant used forswarming.Here, there is a scope to fuzzify the variable C(i) for arriving at
the optimum value of the step size for the given problem in lesstime. Initially the run length vector C(i) value is selected by randomselection and it plays an important role in the convergence of SBF. Asmall value of C(i) causes slow convergence, whereas a large valuemay fail to locate the minima by swimming through them withoutstopping. The selection of C(i) is tedious and time consuming in SBF[18]. Hence, fuzzy adaptive scheme is utilized to C(i) for ensuringthe convergence of SBF algorithm. Here, the fuzzy input variablesare taken as C(i) and the error from the objective function to obtainthe fuzzy output as �C(i) for optimal value. The fuzzy toolbox of
MATLAB 7.01 package on Windows environment is employed tofuzzify the run length vector C(i).
The procedure to create fuzzy logic rules using fuzzy logic tool-box in MATLAB is as follows:
lied So
).
C. Venkaiah, D.M. Vinod Kumar / App
Step a. Type fuzzy in command window of MATLAB to open fuzzylogic toolbox.Step b. Here fuzzy rules have to be presented with inputs to getoutput. To add an input variable Go to Edit menu activate AddVariable and select Input.Step c. Assign desired names to Input and Output variables.Step d. To choose the desired membership function and specifyrange for a particular variable double click on the vari-able block to open a separate membership function editorwindow.Step e. Now Add fuzzy logic rules by opening rule editor window– Activate Edit for fuzzy Rules.Step f. Now Fuzzy block has been created. Assign a name to it andsave the block.Step g. To include fuzzy block created in a MATLAB programinclude following code in the main algorithm.variable = readfis(fuzzy block name);output variable = evalfis([input1, input2, . . .], variable);
Step 2. Iterative algorithm for optimization: the algorithm thatmodels bacterial population chemotaxis, swarming, reproduction,and elimination & dispersal is given here (initially, j = k = l = 0). Forthe algorithm, note that updates to the �i automatically result inupdates to P.
i) Elimination-dispersal loop: l = l + 1.ii) Reproduction loop: k = k + 1.
iii) Chemotaxis loop: j = j + 1.a. For i = 1,2, . . ., S, take a chemotactic step for bacterium i as
followsb. Compute Jerror(i,j,k,l).
Let Jerror(i,j,k,l) = Jerror(i,j,k,l) + Jcc(�i(j,k,l),P(j,k,l))c. Let Jlast = Jerror(i,j,k,l) to save this value since we may find a
better cost via a rund. Tumble: generate a random vector �(i) ∈ Rp with each ele-
ment �m(i), m = 1,2, . . ., p, a random number on [−1,1].e. Move: let �i(j + 1, k, l) = �i(j, k, l) +
C(i)(�(i)/√
�T (i)�(i)).This results in a step of size C(i) in the direction of the
tumble for bacterium i.f. Compute Jerror(i,j + 1,k,l), and then
use this �i(j + 1,k,l) to compute the new Jerror(i,j + 1,k,l) as wedid in f.
Else, let m = Ns. This is the end of while statementj. Go to next bacterium (i + 1) if i /= S (i.e. go to b) to process
the next bacterium.iv) If j < Nc, go to chemotaxis loop (3) of Step 2. In this case, con-
tinue chemotaxis, since the life of the bacteria is not overv) Reproduction:
a. For the given k and l, and for each i = 1,2, . . ., S, let Jihealth
=∑Nc+1j=1 Jerror(i, j, k, l) be the health of bacterium i (a measure
of how many nutrients it got over its life time and how suc-cessful it was at avoiding noxious substances). Sort bacteriaand chemotactic parameters C(i) in order of ascending costJhealth (higher cost means lower health)
b. The Sr bacteria with the highest Jhealth values die and theother Sr bacteria with the best values split (and the copiesthat are made are placed at the same location as their par-ent).
ft Computing 11 (2011) 4921–4930 4929
vi) If k < Nre, go to reproduction loop (2) of step 2. In this case, wehave not reached the number of specified reproduction steps,so we start the next generation in the chemotactic loop.
vii) Elimination-dispersal: for i = 1,2, . . ., S, with probability ped,eliminate and disperse each bacterium (this keeps the num-ber of bacteria in the population constant). To do this, if youeliminate a bacterium, simply disperse one to a random loca-tion on the optimization domain.
viii) If l < Ned, then go to elimination-dispersal loop (1) of step 2;otherwise end.
Appendix B. Objective function of Optimal Power Flow(OPF) problem
B.1. OPF problem formulation
The objective function [22] corresponding to the production costcan be approximated to be a quadratic function of the active poweroutputs from the generating units. Symbolically, it is representedas
minimize Fcos tt =
NG∑i=1
fi(Pi)
where fi(Pi) = aiP2i + biPi + ci, i = 1, 2, . . . , NG
is the expression for cost function corresponding to ith generatingunit and ai, bi and ci are its cost coefficients. Pi is the real poweroutput (MW) of ith generator. NG is the number of online generatingunits.
This constrained OPF problem is subjected to a variety of con-straints depending upon assumptions and practical implications.These include power balance constraints to take into account theenergy balance; feasibility of real and reactive power generation,voltage limits at load buses and line flow limits.
B.1.1. Power balance constraintsThis constraint is based on the principle of equilibrium between
total system generation and total system loads. That is given by setof non-linear power flow equations as
PGi− PDi
−n∑
j=0
|Vi||Vj||Yij| cos(�ij − ıi − ıj) = 0
QGi− QDi
−n∑
j=0
|Vi||Vj||Yij| sin(�ij − ıi − ıj) = 0
where PGi and QGi are the real and reactive power injections at ithbus respectively. The corresponding load demands are given by PDiand QDi. The magnitude and angle of bus admittance matrix is givenas |Yij| and �ij respectively.
The real power loss in the system can be modeled as
Ploss =Nl∑
k=1
gk
[|Vi|2 + |Vj|2 − 2|Vi||Vj| cos(ıi − ıj)
]
Where k is the line connected between buses i and j and corre-sponding conductance is given by gk.
4 lied So
B
br
P
Q
Wou
B
cbb
V
w
B
l
S
w
B
pp
P
wstta
J
w
R
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[rithm for economic load dispatch with non-convex loads, in: Proceedings of the
930 C. Venkaiah, D.M. Vinod Kumar / App
.1.2. The generator constraintsThe output power of each generating unit has a lower and upper
ound so that it lies in between these bounds. This constraint isepresented by a pair of inequality constraints as follows.
minGi ≤ PGi ≤ Pmax
Gi
minGi ≤ QGi ≤ Q max
Gi
here PminGi
and PmaxGi
are lower and upper bounds for real powerutputs of the ith generating unit. Q min
Giand Q max
Giare lower and
pper bounds for reactive power outputs of the ith generating unit.
.1.3. Voltage limitsThe voltage magnitudes of the each and every load buses after
onducting the load flow simulation should be verified between itsounds. This voltage magnitude is having its own lower and upperound and mathematically represented by
mini ≤ Vi ≤ Vmax
i
here Vmini
and Vmaxi
are lower and upper bounds of the voltages.
.1.4. Transmission line loadingsThe line flows of all the transmission lines should be within its
ine capacity given by MVA ratings. This can be given as
L ≤ SmaxL
here SmaxL is the line flow capacity of Lth transmission line.
.2. OPF constraints handling
The equality and inequality constraints of the power dispatchroblem are considered in the fitness function (Jerror) itself by incor-orating a penalty function.
Fi ={
ki(Ui − Ulimi
)2
if violated0 otherwise
here ki is the constant, called penalty factor for the ith con-traint. Now the final solution should not contain any penalty forhe constraint violation. Therefore the objective of the problem ishe minimization of generation cost and penalty function due tony constraint violation as defined by the following equation.
error = Fcos tt +
nc∑i=0
PFi
here “nc” is the number of constraints.
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