ba

ndiaIndi

Bacterial foraging techniqueClassical controller

utol cl(PIDperin

c re

(K and K ) and speed regulation parameters (R) by BF technique which surprisingly has not been

ided inroughhem. Tupportystem

performance of I, PI, ID, PID and integraldouble derivative (IDD)are tried and their performances compared so as to assess the bestcontroller in [10]. But their investigations limited to thermal sys-tem only. How these classical controllers perform in multi-areahydrothermal system? Literature survey does not provide any an-swer to this question.

manipulates the representation of potential solution, rather thanthe solutions itself [7]. Only two operations such as cross overand mutation are performed to overcome the possibility of beingtrapped into local minimum in GA. Some of deciencies in GAperformance, like premature convergence which again degradesits efciency and reduces the search capability has been pointedout in [7]. Some of the search techniques like Bacterial Foragingtechnique (BF) [7,8], Particle Swarm optimization (PSO), etc. arealso available [9,11] for optimization of several parameters.PSO is developed through simulation of bird ocking in

Corresponding author. Tel.: +91 9435173835; fax: +91 3842 233797.E-mail addresses: lcsaikia@yahoo.com (L.C. Saikia), nidulsinha@hotmail.com (N.

Electrical Power and Energy Systems 45 (2013) 98106

Contents lists available at

n

.e lSinha), janardannanda@yahoo.co.in (J. Nanda).to change in loading, change in parameters of the system andany other abnormal conditions. Many investigations [122] inthe area of automatic generation control (AGC) of interconnectedpower system have been reported in the past. Many of them areassociated with AGC of two equal area thermal systems. Sincepractical interconnected systems are multi-area and most of thecases hydrothermal. Surprisingly little attention has been paid tomulti-area hydrothermal system. In most of the earlier literatures[110] some common classical controllers such as integral (I), pro-portional plus integral (PI), integral plus derivative (ID) and pro-portional plus integral plus derivative (PID) have been used. The

[1318] and articial neural network (ANN) controller [1719]for better dynamic performance in the AGC system. Fuzzy Integral,Fuzzy PI and Fuzzy PID controllers have been discussed in [1416].But, no literature reported in the past concerned with Fuzzy inte-gral plus double derivative controller (FIDD).

Only two techniques namely genetic algorithm (GA) andclassical technique based on integral square error (ISE) are usedin the earlier literatures in AGC for the design of Fuzzy integral,Fuzzy PI and Fuzzy PID controllers. GA explores many search spacerather than single region effectively and hence it is less sensitive tolocal minimum as compared to conventional approach and GAFuzzy integral double derivative controllerIntegral double derivative controller

1. Introduction

Large scale power systems are divareas and they are interconnected thcontractual power exchange among ttem also provides the inter-area soperations. The tie line power and s0142-0615/$ - see front matter 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijepes.2012.08.052I D

attempted in the past for the system provides not only the best dynamic response for the system but alsoprovides higher values of R, that will appeal for easier and cheaper realization of the governor.

2012 Elsevier Ltd. All rights reserved.

to numbers of coherenttie lines to facilitate forhis interconnected sys-during the abnormal

frequency changes due

An I or PI or ID or PID or IDD controller optimized at a particularoperating condition may not perform satisfactorily when there is achange in operating condition [3]. Moreover, the non-linear natureof AGC problem makes it difcult to ensure stability at all operat-ing conditions with classical integral or PI or PID controllers beingoptimized at a particular operating condition [4]. Some investiga-tions have been carried out using fuzzy logic controller (FLC)Keywords:Automatic generation control

better dynamic performance than the later. Sensitivity analysis has been performed to nd the robust-ness of the FIDD controller for wide change in loading. Simultaneous optimization of IDD controller gainsMaiden application of bacterial foragingof a multi-area hydrothermal system

Lalit Chandra Saikia a,, Nidul Sinha a, J. Nanda baDepartment of Electrical Engineering, National Institute of Technology Silchar, Assam, IbDepartment of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi,

a r t i c l e i n f o

Article history:Received 4 August 2010Received in revised form 23 August 2012Accepted 29 August 2012Available online 6 October 2012

a b s t r a c t

This paper dealt with the aThe performance of severationalintegralderivativeIDD controller gives betteraging (BF) optimized fuzzyComparison of the dynami

Electrical Power a

journal homepage: wwwll rights reserved.sed fuzzy IDD controller in AGC

a

matic generation control of an unequal multi-area hydrothermal system.assical controllers such as integral (I), proportionalintegral (PI), propor-) and integraldouble derivative (IDD) are compared, and it is found thatformance over the other controllers. A maiden application of Bacterial For-tegraldouble derivative (FIDD) controller has been made in the system.sponses of the system for FIDD and IDD reveals that FIDD controller gives

SciVerse ScienceDirect

d Energy Systems

sevier .com/locate / i jepes

gains respectively

nd Emulti-dimensional space. Like GA, PSO is also less susceptible togetting trapped on local optimum [12]. The authors in [12] haveshown that performance of BF is better than PSO in terms of con-vergence, robustness and precision. Though, both BF and PSO tech-niques are used for optimization of secondary controller gains andsome other parameters in AGC [79], surprisingly they are notused for design of any Fuzzy logic controller which needs furtherinvestigations.

In almost all the past literature on Fuzzy logic controller in AGC,more attention has been paid to the design of the controller butnever investigate the controller performance in different loadingconditions which are generally occurs in the system.

Almost all the past works centred on the design of secondary or

Nomenclature

f nominal system frequency (Hz)i subscript referred to area i (13) superscript denotes optimum valuePri rated power of area i (MW)Hi inertia constant of area i (s)DPgi incremental generation change in area i (p.u)Di DPDi/Dfi (p.u/Hz)T12, T23, T13 synchronizing coefcientsRi governor speed regulation parameter of area i (Hz/p.u

MW)Tgi steam governor time constant of area i (s)Kri steam turbine reheat coefcient of area iTri steam turbine reheat time constant of area i (s)Tti steam turbine time constant of area i (s)Bi frequency bias constant of area iTpi 2Hi/(f Di)Kpi 1/Di (Hz/p.u)bi area frequency response characteristics of area i

(=Di + 1/Ri)

L.C. Saikia et al. / Electrical Power asupplementary controllers and surprisingly little attention havebeen paid to the design of primary controller, i.e., selection of prop-er governor speed regulation parameters (R). It is known that withonly primary control (i.e. secondary or supplementary control ab-sent) the smaller the governor drop the smaller the steady state er-ror in frequency but in the presence of supplementary controlthere is nothing to be sacrosanct about a small governor droop(of the order of 46% used in practice) and for any large but cred-ible value of R, zero steady state error in frequency is guaranteed. Afew works [57,10] have been reported to an extent selection ofgovernor speed regulation parameter R. A comprehensive approachor optimization procedure has been provided for selection of suit-able value of R in [7] using BF technique. But till date no suchinvestigations have been (i.e., optimization of R parameters) donein multi-area area hydrothermal system. In view of the above,the objectives of the present works are

(a) Optimization of classical I, PI, PID, IDD controllers gainsusing BF technique with Ri = 2.4 in multi-area hydrothermalsystem and to Comparison of dynamic responses for theabove controllers to get the best controllers.

(b) Design of a new bacterial foraging optimized fuzzy logic con-troller named as fuzzy logic based integral double derivative(FIDD) controller and to compare the dynamic responses ofthe system for the best classical controller found in (a) andFIDD controller.

(c) Sensitivity analysis of the IDD and FIDD controller in the sys-tem investigated for different loading conditions.(d) Simultaneous optimization of IDD controller gains and Rparameters to obtain better dynamic performance and foreasier and cheaper realization of the governor.

2. System investigated

Investigations have been carried out on a three unequal area hy-dro-thermal system of area 1: 2000 MW, area 2: 6000 MW, area3:10,000 MW. The area 1 and area 2 are thermal systems and area3 is a hydro system provided with electric governor. Thermal areasare provided with single reheat turbine. Generation rate con-straints (GRC) of 3% per minute in thermal areas and 270% per min-ute for raising and 360% per minute for lowering generation in

p number of parameters to be optimizedS number of bacteriaNS swimming length after which tumbling of bacteria will

be undertaken in a chemotactic loopNC number of iterations to be undertaken in a chemotactic

loop (NC > NS)Nre maximum number of reproduction to be undertakenNed maximum number of elimination and dispersal eventsPed probability with which elimination and dispersal will

continueTw water starting time for hydro turbine (s)Dfi incremental change in frequency of area i (Hz)DPgi incremental generation of area i (p.u)DPtie ij incremental change in tie line power connecting be-

tween area i and area j (p.u)Kd, Kp, Ki electric governor derivative, proportional, and integral

nergy Systems 45 (2013) 98106 99hydro area are considered. The optimum values of integral gainKi, proportional gain Kp and derivative gain Kd of electric governorand other parameters of hydro area are taken from [6] and thenominal parameters of the thermal systems are taken from [10]and given in Appendix. The classical controllers like I, PI, PID andIDD are considered separately with the system. The classical con-trollers are replaced by FIDD controller to study the dynamic per-formances. Per unit values of different parameters of the threeunequal areas are considered to be same on their respective bases.Hence, while modeling interconnected areas of different capacities,a parameter a12 = Pr1/Pr2, a23 = Pr2/Pr3 and a13 = Pr1/Pr3 are con-sidered in the three area system. The transfer function model of thesystem with FIDD controller is shown in Fig. 1. The system dy-namic performance is evaluated by considering 1% step load per-turbation (SLP) in area 1.

3. Bacterial foraging optimization technique

Bacterial Foraging (BF) technique is a powerful evolutionaryoptimization technique proposed by Passino [23] in which thenumber of parameters that are used for searching the total solutionspace is much higher compared to those in GA. In BF technique, theforaging behavior of Escherichia coli bacteria present in our intes-tine is mimicked. The control system of these bacteria that dictateshow foraging should proceed can be subdivided into four sectionsnamely chemotaxis, Swarming, Reproduction and Elimination anddispersal.

with Fuzzy integral double derivative (FIDD) controller.

nd EThe chemotaxis process is achieved through swimming andtumbling via Flagella of the E. coli bacteria. The rotation of Flagellain each bacterium decides whether it should move in a predeneddirection (swimming) or altogether in different directions (tum-bling), in the entire lifetime. A unit length random direction, say/(j), is generated to represent a tumble and this will be used to de-ne the direction of movement after a tumble.

In particular hij 1; k; l hij; k; l Ci/j 1

where hi(j,k, l) represents the ith bacterium at jth chemotactic, kthreproductive and lth elimination and dispersal step. C(i) is the sizeof the step taken in the random direction specied by the tumble(run length unit).

During foraging the bacterium which reached optimum path forfood location provides an attraction signal to other bacteria so that

Fig. 1. Transfer function model of three area system

100 L.C. Saikia et al. / Electrical Power athey can swarm together in a group to reach the desired location.This is the swarming process and mathematically is represented by

Jcch; Pj; k; l XSi1

Jicch; hij; k; l

XSi1

dattract exp xattractXpm1

hm him 2 !" #

XSi1

hrepelent exp xrepelentXpm1

hm him 2 !" #

2

where Jcc(h,P(j,k, l)) is the cost function value to be added to the ac-tual cost function to be minimized to present a time varying costfunction. S is the total number of bacteria and p the number ofparameters to be optimized which are present in each bacterium.dattract, xattract, hrepelent, xrepelent are different coefcients that are tobe chosen properly.

During reproduction the least healthy bacteria die and the otherhealthiest bacteria each split into two bacteria, which are placed inthe same location. This makes the population of bacteria constant.

The live of a population of bacteria may changes in the localenvironment and this change may be gradual or sudden due to dif-ferent reasons. Such type of event may occur where all the bacteriain a region killed (or eliminated) or a group is dispersing into a newpart of the environment. Thus, there is the possibility of destroyingnergy Systems 45 (2013) 98106the chemotactic process, but also have the effect of assisting inchemotaxis, since dispersal may place bacteria near good foodsources. Thus, elimination and dispersal are parts of the popula-tion-level long-distance motile behavior.

The detail algorithm is presented in [7]. In this paper, only theow chart of BF algorithm is presented and shown in Fig. 2. In thissimulation work we have considered S = 6, Nc = 6, Ns = 3, Nre = 20,Ned = 2, Ped = 0.25, dattract = 0.01, xattract = 0.04, hrepelent = 0.01 andxrepelent = 10. The value of p is equal to the number of parametersto be optimized.

Fig. 2. Flow chart for bacterial foraging optimization.

Fig. 3. Structure of fuzzy logic based Integral Double Derivative (FIDD) controller.

4. Bacterial foraging optimized fuzzy logic based integraldouble derivative (FIDD) controller

Because of non-linear nature of AGC problem, the conventionalclassical controller may not give the satisfactory solution. Therobustness and reliability of fuzzy logic controller (FLC) make thiscontroller an ideal choice for solving the AGC problem. Fuzzy logicbased integral, PI and PID controllers have been presented in mostof the literature as the secondary controller. In this paper a FIDD ispresented for the rst time in AGC of a multi-area hydrothermalsystem. The structure of FIDD is shown in Fig. 3.

The structure comprises of fuzzy logic controller and a conven-tional IDD controller in series. The fuzzy logic controller has twoinputs signals, namely ACE and ACE. The output signal of the fuzzylogic controller (x) is the input to the conventional IDD controller.The output of the IDD controller is the control signal (u) for theplant.

There are four components of fuzzy logic controller. They arethe fuzzier, the inference engine, the rule base and the defuzzier.The fuzzier transforms the numeric into fuzzy sets. The inference

Table 1Control rule for FIDD controller.

ACE NB NM NS ZE PS PM PBNB PB PB PB PM PM PS ZENM PB PB PB PB PM PS NSNS PB PB PB PM ZE NS NMZE PB PB PB ZE NS NM NBPS PM PS ZE NS NS NM NBPM PS ZE NS NM NM NM NBPB ZE NS NM NM NB NB NB

Fig. 5. Membership functions for FIDD controller.

L.C. Saikia et al. / Electrical Power and Energy Systems 45 (2013) 98106 101Fig. 4. Comparison of I, PI, PID and IDD controller performance in the system. (a) Frequency deviation in area 1 versus time. (b) Frequency deviation in area 2 versus time. (c)Deviation in the tie line power connecting between area 1 and area 2 versus time.

Table 2Numerical values of peak overshoots and settling times of Fig. 4.

Fig. no. Response Peak overshoot Settling time

I PI PID IDD I PI PID IDD

4a Df1 0.02158 0.01855 0.01777 0.02203 89.01 80.03 84.96 62.824b Df2 0.01388 0.01275 0.01231 0.01363 72.11 84.48 78.69 65.014c DPtie12 0.00106 0.00082 0.00034 0.00113 88.49 92.97 66.95 57.04

Fig. 6. Comparison of IDD and FIDD controller performancfe. (a) Frequency deviation in area 1 versus time. (b) Frequency deviation in area 2 versus time. (c) Frequencydeviation in area 3 versus time. (d) Deviation in the tie line power connecting between area 1 and area 2 versus time. (e) Deviation in the tie line power connecting betweenarea 2 and area 3 versus time.

102 L.C. Saikia et al. / Electrical Power and Energy Systems 45 (2013) 98106

engine performs all the logical manipulations. The rule base con-sists of membership functions and control rules. The output ofthe fuzzy inference engine is the fuzzy set which is transformedinto numeric value by defuzzication process. The control outputof FIDD controller is given by

ut Z

KIixdt KDid2x

dt2

!3

For designing the FIDD controller, the IDD controller gains,membership functions and control rules are to be determined. Inthis paper seven numbers of Gaussian membership functions aretaken for both inputs and output. The control rules are taken from[16] and shown in Table 1. For the fuzzy logic controller shown inFig. 3, a mamdani type fuzzy inference system (FIS) with min asand method, max as or method and centroid as defuzzicationmethod are taken. For this FIDD controller, the integral gains KIi,and double derivative gain (K ) for FIDD controller and left base,

I1 I2 I3

of PI controller gains are KI1 0:3961, KI2 0:0344, KI3 0:0025,KP1 0:1359, KP2 0:1503 and KP3 0:1148. The optimum valueof PID controller gains are KI1 0:3027, KI2 0:3425,KI3 0:0237, Kp1 0:0141, Kp2 0:01415, Kp3 0:0234,KD1 0:009, KD2 0:0462 and KD3 0:0043. The optimum valuesof IDD controller gains are KI1 0:4633, KI2 0:1827,KI3 0:0141, KD1 0:0105, KD2 0:0104 and KD3 0:0021. Thecomparisons of dynamic responses of the above controllers areshown in Fig. 4ac. The peak deviations in the responses corre-sponding each controller are more or less same. The peak over-shoots and settling time of the responses are noted and shown inTable 2. The settling time of the responses corresponding to IDDcontroller is less than the others. Though the peak overshoot of

Table 3Numerical values of peak overshoots and settling times of Fig. 6.

Fig. no. Response Peak overshoot Settling time

IDD FIDD IDD FIDD

6a Df1 0.02142 0.01554 60.26 49.756b Df2 0.01335 0.01071 64.81 52.766c Df3 0.01081 0.00742 65.47 55.216d DPtie12 0.00113 0.00059 61.00 51.376e DPtie23 0.00117 0.00069 73.63 58.75

L.C. Saikia et al. / Electrical Power and Energy Systems 45 (2013) 98106 103Di

right base and center of each Gaussian membership are the vari-ables and they are optimized using BF technique. In case of BF tech-nique we assign each bacterium with a set of variables to beoptimized and are assigned with random values (D) within theuniverse of discourse dened through upper and lower limit be-tween which the optimum value is likely to fall. In our case, theintegral gains KIi, and double derivative gain (KDi) for FIDD control-ler and left base, right base and center of each Gaussian member-ship are the variables to be optimized. Each Bacterium is allowedto take all possible values within the range and the objective func-tion which is ISE dened by (4) is minimized.

5. Result and analysis

Simulink models for the proposed system and different pro-grammes are developed in Matlab 7.01 to obtain dynamic re-sponses for Dfi and DPtie ij for 1% SLP in area 1.

5.1. Simulation of the system with classical controllers

Controllers such as I, PI, PID and IDD are examined separately inthe system and their gains are optimized by BF technique. The per-formance index used in this optimization is integral square error(ISE) as given by

J Z T0

Dfi2 DPtieij2n o

dt 4Fig. 8. (a) Frequency deviation in area 1 versus time for 30% loading for IDD and FIDD cFIDD controller.The optimum values of integral controller gains are found toK 0:4318; K 0:2251 and K 0:0012. The optimum value

Fig. 7. Convergence characteristics of BF, PSO and GA algorithm.ontroller. (b) Frequency deviation in area 1 versus time for 90% loading for IDD and

Table4

Num

erical

values

ofPeak

Oversho

ots(POs)

andSettlin

gTimes

(STs)of

Fig.

8.

Fig.

7afor30

%load

ing

Fig.

8bfor90

%load

ing

IDDwithop

timum

gainscorrespo

ndingto

50%load

ing

FIDDwithsetting50

%load

ing

IDDwithop

timum

gainscorrespo

ndingto

50%load

ing

FIDDwithsettingcorrespo

ndingto

50%load

ing

STPO

STPO

STPO

STPO

TillT

0.02

1256

.20.01

802

49.23

0.01

835

39.37

0.01

239

104 L.C. Saikia et al. / Electrical Power and Ethe responses for IDD controller is slightly more than that of oth-ers, the magnitude of oscillations is less for IDD controller. Thus,it is seen that the IDD controller is best among the others fromthe point of view of settling time and magnitude of oscillation.Only three dynamic responses are shown (Fig. 4) to justify thestatement. Hence further studies are carried out considering onlyintegraldouble derivative controllers and the newly proposed fuz-zy logic based integraldouble derivative (FIDD) controllers.

5.2. Simulation of the system using bacterial foraging optimized fuzzylogic based integral double derivative controller (FIDD)

Now, the IDD controllers from the system are replaced by FIDDcontroller. For this FIDD controller, the integral gains KIi, and dou-ble derivative gain (KDi) for FIDD controller and left base, right baseand center of each Gaussian membership are the variables opti-mized using BF technique. The optimized left base and right baseof each membership for input and outputs are shown in Fig. 5.The optimum values of IDD gains of FIDD controller obtained byBF technique are KI1 1:999, KI2 0:0028, KI3 1:1786,KD1 0:05221, KD2 0:00017 and KD3 0:0000272. Using theoptimised FIDD above, the dynamic responses are obtained andcomparison of these dynamic responses with that of IDD controllerare shown in Fig. 6ae. The settling time and peak overshoot ofeach responses of Fig. 6 are noted and shown in Table 3. Fromthe table it is clearly seen that the settling time and peak overshootis less for FIDD controller. It is also clear from Fig. 6 that the mag-nitude of oscillations are less in the responses corresponding toFIDD controller. Thus, FIDD controller provides better dynamic per-formance than IDD controller from the viewpoint of settling time,peak overshoot and magnitude of oscillations. Only ve dynamicresponses are shown to justify the statement. The convergencecharacteristics of BF, PSO and GA are depicted in Fig. 7 where num-ber of J evaluations are as abscissa and Minimum value of J as ordi-nate. It is quite clear that from among the three techniques theconvergence of BF is the fastest though the nal value of cost func-tion is almost same. Hence, a faster converging algorithm will re-duce computational burden.

5.3. Sensitivity analysis for the IDD and FIDD controller at changedloading condition

The robustness of the FIDD controller for different loading (30%,40%, 70% and 90%) conditions is also investigated. Fig. 8a and bshows the dynamic responses forDf1 = f(t) for 30%, and 90% loadingfor IDD and FIDD controllers. Examining Fig. 8, the settling timeand peak overshoots are noted and shown in Table 4. The over-shoot and settling time corresponding to FIDD controller is lessthan that of IDD controller. Thus, FIDD controller performed wellin changed loading condition also. Here, only two dynamic re-sponses are shown.

5.4. Selection of speed regulation parameters in multi-areahydrothermal system

The system is provided with IDD controller, the integral gain KIi,double derivative gain KDi of the IDD controllers and speedregulation parameters (Ri) are optimised using BF technique. Theoptimum values of IDD controllers gains and speed regulationparameters are KI1 0:3762, KI2 0:0369, KI3 0:0361, KD1 0:0493, KD2 0:0059 and KD3 0:001, R1 8:2884 13:8%,R2 8:8599 14:8%, R3 7:4302 12:4%. The dynamic re-sponses corresponding to these optimum values are compared

nergy Systems 45 (2013) 98106with the responses corresponding to KI1;KDi with Ri = 2.4 (=4%droop) and shown in Fig. 9. The settling time and peak overshootof the responses are noted from Fig. 9 and shown in Table 5.

nd EL.C. Saikia et al. / Electrical Power aThough the values of peak overshoot slightly less and settling timeis slightly more for the responses corresponding to Ri Ri thanthat corresponding to Ri = 2.4, practically not much difference.Also, the magnitude of oscillations are less for responses corre-sponding to Ri Ri . It is also seen that when we optimize IDDcontroller gains and speed regulation parameters simultaneously,we obtain much higher values of Ri than when Ri = 2.4 which facil-itate simple and cheaper realization of the governor.

6. Conclusion

The integraldouble derivative (IDD) controller has been ap-plied for the rst time in AGC unequal area hydrothermal systemwhich provides much better performance than Integral (I), propor-tionalintegral (PI), and proportionalintegralderivative (PID)

Table 5Numerical values of Peak Overshoots (POs) and Settling Times (STs) of Fig. 9.

Fig. no. Response IDD controller with

Ri = 4% Ri RiPO ST PO ST

9a Df1 0.02203 67.95 0.01363 70.769b Df2 0.01363 69.59 0.0066 72.989c DPtie12 0.00129 55.72 0.0012 60.95

Fig. 9. Comparison of dynamic responses of the system for IDD controller between KIi;Ktime. (b) Frequency deviation in area 2 versus time. (c) Deviation in tie line power in thnergy Systems 45 (2013) 98106 105controllers. The performances for I, PI and PID controllers are prac-tically the same from the view point of dynamic responses in mul-ti-area hydrothermal system. A maiden attempt has been made touse bacterial foraging optimized fuzzy logic based integraldoublederivative (FIDD) controller in AGC which provides much betterperformance than classical integraldouble derivative (IDD) con-troller in automatic generation control of an unequal multi-areahydrothermal system. The FIDD controller set at nominal conditionof 50% loading is quite robust for wide change in loading from thenominal. Simultaneous optimization of KIi, KDi and Ri provides notonly the better dynamic response for the system but also revealsthat different areas can have different optimum values of R andseveral areas may have much higher values of R, with some areaeven having a value close to 5 times the value of 4% used in prac-tice. Such high values of R obtained from simultaneous optimiza-tion are recommended for adoption in practice for easy andcheaper realization of governors.

Appendix A

Nominal parameters of the system investigated

f 60 Hz; Tgi 0:08 s; Tri 10 s; Hi 5; s;Tti 0:3 s; Kr 0:5;Ptie;ijmax 200 MW; Tpi 20 s; Kd 4:0; Kp 1:0; Ki 5:0;Di 0:00833 p:u:MW=Hz; Kpi 120 Hz=p:u MW; Tw 1 s;initial loading 50%

Di with Ri = 2.4 (=4% droop) and K

Ii; K

Di; R

i . (a) Frequency deviation in area 1 versus

e line connecting between area 1 and area 2 versus time.

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106 L.C. Saikia et al. / Electrical Power and Energy Systems 45 (2013) 98106

Maiden application of bacterial foraging based fuzzy IDD controller in AGC of a multi-area hydrothermal system1 Introduction2 System investigated3 Bacterial foraging optimization technique4 Bacterial foraging optimized fuzzy logic based integral double derivative (FIDD) controller5 Result and analysis5.1 Simulation of the system with classical controllers5.2 Simulation of the system using bacterial foraging optimized fuzzy logic based integral double derivative controller (FIDD)5.3 Sensitivity analysis for the IDD and FIDD controller at changed loading condition5.4 Selection of speed regulation parameters in multi-area hydrothermal system

6 ConclusionAppendix AReferences