International Journal of Engineering, Science and Technology Vol. 2, No. 3, 2010, pp

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1 MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol., No. 3, 1, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY 1 MultCraft Lmted. All rghts reserved Overall performance evaluaton of evolutonary desgned conventonal AGC controllers for nterconnected electrc power system studes n a deregulated market envronment Y.L. Karnavas*, K.S. Dedouss Lab. of Electrc Machnes & Installatons, Dept. of Electrcal Engneerng School of Appled Technology, Technologcal Educatonal Insttuton of Crete (TEIC), PO Box 1939, Zp 71 4, Heraklon, Crete, Hellas, GREECE * Correspondng Author: e-mal: karnab@staff.tecrete.gr Abstract Electrc power ndustry s currently n transton from vertcally ntegrated utltes to an ndustry that wll ncorporate compettve companes. Ths ncreases the complexty of the load frequency ssue and calls for more nsght and research. In ths context, the tunng of a mult-area automatc generaton control (AGC) system after deregulaton and furthermore, the effect of reheat turbnes dynamcs n the power system performance, are not yet dscussed n depth and are studed n ths work. The effect of blateral contracts on the dynamcs of the system s taken nto account and the concept of DISCO partcpaton matrx for these blateral contracts s smulated. Genetc algorthms are adopted n order to obtan the optmal parameters of the loadfrequency controllers as well as of the frequency bases of thermal systems wth reheat turbnes. Also, snce the optmum parameter values of the classcal AGC have been obtaned n the lterature by mnmzng the popular ntegral of the squared errors crteron (ISE) only, an effort s made n ths study to show that ths crteron does not gve always the best system performance especally n a deregulated envronment. In ths work, we nvestgate the optmum adjustment of the load frequency controllers usng a set of performance ndces whch are varous functons of error and tme. In ths way, someone can observe the varous performances that such a knd of power system mght have when a dfferent performance ndex s used. It should be noted that to the extent of the authors' knowledge, ths knd of optmzaton has not been done yet n the lterature. The performances of the tuned two area AGC system are obtaned usng approprate Matlab/Smulnk models. Fnally, t s envsaged that the synthess procedure hghlghted n ths paper could be of practcal sgnfcance for tunng conventonal AGC controllers for an nterconnected thermal-electrc power system n a deregulated envronment. Keywords: AGC, load frequency control, power systems, deregulaton, blateral contracts, genetc algorthms 1. Introducton Many nvestgatons have been reported n the past pertanng to AGC of a large nterconnected power system (.e Abdel-Magd and Dawoud, 1997, Adtya and Das, 3, Cohn, 1986). A net nterchange te-lne bas control strategy has also been wdely accepted by utltes. The frequency and the nterchanged power are kept at ther desred values by means of feedback of the area control error (ACE) ntegral, contanng the frequency devaton and the error of the te-lne power, and controllng the prme movers of the generators. The controllers so desgned regulate the ACE to zero. For each area, a bas constant determnes the relatve mportance attached to the frequency error feedback wth respect to the te-lne power error feedback; the bas s very often equal to the natural area frequency response characterstc. Classcal AGC corresponds bascally to ndustry practce for the past years or so. The key assumptons are: the steady-state frequency error followng a step-load change should vansh and also the transent frequency and tme errors should be small, the statc change n the te power followng a step-load n any area should be zero, provded each area can accommodate ts own load change and any area n need of power durng emergency should be asssted from other areas. The key advantage of the classcal AGC s that the control strategy s a totally decentralzed one, n the sense that each control area carres out ts own frequency and power regulaton usng locally gathered real-tme nformaton.

2 151 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp On the other hand, the tradtonal power system ndustry has a vertcally ntegrated utlty structure. In the restructured or deregulated envronment, vertcally ntegrated utltes no longer exst. The utltes no longer own generaton, transmsson, and dstrbuton; nstead, there are three dfferent enttes, vz., GenCos (generaton companes), TransCos (transmsson companes) and DsCos (dstrbuton companes). As there are several GenCos and DsCos n the deregulated structure, a DsCo has the freedom to have a contract wth any GenCo for transacton of power. A DsCo may have a contract wth a GenCo n another control area. Such transactons are called blateral transactons. All the transactons have to be cleared through an mpartal entty called an ndependent system operator (ISO). The ISO has to control a number of so-called ancllary servces, one of whch s AGC. For an n-depth dscusson of mplcatons of restructurng the power ndustry, the reader can refer to (Ilc et al, 1998, Sheble, 1999, Chrste et al, ). So, t s obvous nowadays that n a restructured electrc power system envronment, the engneerng aspects of plannng and operaton have to be reformulated. In most of the recent reported strateges, attempts have been made to adapt well-tested classcal AGC schemes to the changng envronment of power system operaton under deregulaton (Kumar et al, 1997, Delfno et al,, Ibraheem et al, 9, Snha et al, 1). Comprehensve studes on smulaton and optmzaton n an AGC system after deregulaton have been carred out by Donde et al as well as one of the authors (Donde, 1, Karnavas, 5). In Donde s work the concept of DsCo partcpaton matrx (DPM) s proposed that helps the vsualzaton and mplementaton of the contracts. The crtcal parameters n order to tune such a system are found to be the feedback ntegral gans of the conventonal ntegral controllers as well as the frequency bases of the areas. In ths work, all the three components of proportonal plus ntegral plus dervatve (PID) load frequency controllers are beng examned, and a two-area AGC system block dagram n restructured envronment s used to demonstrate the tunng procedure. Modfcatons are made n the area controllers whch are extended to be I, PI and PID ones as well. A set of dfferent performance ndces whch are varous functons of error and tme s also used here. In ths way, someone can observe the varous performances that such a knd of power system mght have when a dfferent performance ndex s used. It should be noted that to the extent of the authors' knowledge, ths knd of optmzaton has not been done yet n the lterature. The paper s organzed as follows. In the next secton the block dagram of the two-area four-gencos AGC system s modeled, descrbed and ts aspects are dscussed. The reheat type steam turbne model s also mplemented there. GAs detals and the tunng procedure are gven next. The GA tunng s appled to three case studes descrbed n the fourth Secton concernng normal and contract volaton stuatons, and the smulaton results whch are summarzed n ffth secton show the effectveness of the proposed tunng procedure. Fnally, n the concluson Secton, some comments are gven as well as some thoughts for future work.. The Deregulated Market Envronment for AGC The tradtonal AGC s well dscussed n numerous works (.e. Elgerd, 197, Karnavas and Papadopoulos,, Pan and Lan, 5) whle research work n deregulated AGC can be found n (Kumar et al, 1997, Delfno et al,, Donde et al, 1, Chrste and Bose, 1996, Noble et al,, Bevran et al, 4, Karnavas, 5, Shayegh et al, 6, Demroren and Zeynelgl, 7, Srnvasa et al, 8). In the new restructured envronment (see Fgure 1), GenCos sell power to varous DsCos at compettve prces. DsCos have the lberty to choose the GenCos for ther contracts. They may or may not have contracts wth the GenCos n ther own area. Ths makes varous combnatons of GenCo-DsCo contracts possble n practce (Fgure ). The block dagram n Fgure 3 shows how the blateral contracts are ncorporated n the tradtonal AGC system. The system s modeled n Matlab/Smulnk and the area controllers are replaced wth I or PI or PID ones. Each area ncludes two dentcal GenCos and two DsCos. Wth respect to Fgure 3, the four loads of the DsCos are stored n the DISCO block. It should be noted also that the two power systems have equal nomnal nstalled capactes. Furthermore, the developed model for a GenCo s shown n Fgure 4, and the reheater transfer functon block s taken from Kumar et al (1985). Fnally, the used model for the conventonal controllers s shown n Fgure 5. The controller's demand sgnal s dstrbuted accordng to the area partcpaton factors (apf) block. Each GenCo s represented by a governor, a reheater and a turbne. All the system data are gven for clarty n the Appendx A. A r e a I A re GC #1 GC # GC #ν ΤC #1 ΤC # ΤC #ν DC #1 GC # GC #ν GC #1 GC # GC #ν I S O GC #1 ΤC #1 DC #1 GC # ΤC # DC # GC #ν ΤC #ν DC #ν A r e a X a ΤC #1 ΤC # ΤC #ν II DC #1 DC # DC #ν Fgure 1. Interconnecton between generaton (GC), transmsson (TC) and dstrbuton (DC) companes n a deregulated envronment operated by ndependent system operator (ISO).

3 15 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp A r e a GenCo Contracts Area Controller DsCo Contracts I A re Power System a II GenCo Contracts Area Controller DsCo Contracts Fgure. Schematc of a two-area AGC model n a restructured envronment. 1/R1 ΔPL1 Δf1 I, PI, PID Controller 1 apf1 1/R Δf1 a11 1/R3 ΔPte Δf a1 I, PI, PID Δf Controller apf ΔPL 1/R4 Fgure 3. Developed model of a two-area double-genco AGC system wth controllers. Fgure 4. Developed model of a GenCo wth a reheat turbne. Fgure 5. Dscrete PID-type controller used n ths study.

4 153 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Dependng on the contracts made between GenCos and DsCos, the DPM s set. DPM s a matrx wth the number of rows equal to the number of GenCos and the number of columns equal to the number of DsCos n the system (see Eq. 1). Each entry n ths matrx can be thought of as a fracton of a total load contracted by j th DsCo towards the th GenCo and s called contract partcpaton factor (cpf) as seen n Eq.. where cpf DC1 DC DC3 DC4 cpf11 cpf1 cpf13 cpf14 GC1 DPM (1) cpf1 cpf cpf3 cpf4 GC cpf 31 cpf3 cpf33 cpf34 GC3 cpf41 cpf4 cpf43 cpf44 GC4 j j th th DsCo's power demand out of GenCo [pu.mw] th j DsCo's total power demand [pu.mw] () Whenever a load demanded by a DsCo changes, t s reflected as a local load n the area to whch ths DsCo belongs. Ths corresponds to the local loads ΔP L1 and ΔP L and should be reflected n the deregulated AGC system block dagram at the pont of nput to the power system block. As there are many GenCos n each area, ACE sgnal has to be dstrbuted among them n proporton to ther partcpaton n the AGC. Coeffcents that dstrbute ACE to several GenCos are termed (as descrbed above) m ACE partcpaton factors (apf). Note that 1 ( ) 1 j apf where m s the number of GenCos. Thus, as a partcular set of GenCos j are supposed to follow the load demanded by a DsCo, nformaton sgnals must flow from a DsCo to a partcular GenCo specfyng correspondng demands. These sgnals (whch were absent from the tradtonal AGC scenaro) descrbng the partal demands, are specfed by the cpfs and the pumw load of a DsCo. These sgnals carry nformaton as to whch GenCo has to follow a load demanded by whch DsCo. In our case of two areas (I, II), the scheduled steady state power flow on the te-lne s gven as scheduled Demand of DsCos n area II from GenCos n area I P te I II Demand of DsCos n area I from GenCos n area II (3) At any gven tme, the te lne power error s defned: P P -P (4) actual, scheduled, te te te Ths error vanshes n the steady state as the actual te lne power flow reaches the scheduled power flow. Ths error sgnal s used to generate the respectve ACE sgnals as n the tradtonal scenaro. Thus, the area control error (ACE) for the th area at any tme nstant t s defned as, ACE t e t P t B f t (5) where te1 r1 r te1 te P P P P and P r1, P r are the rated nstalled capactes of areas I and II, respectvely. Consequently, ACE1 B1f 1 a1 P te 1 and 1 te 1 producton s gven by: ACE B f a P where a 1 P r1 P r. Therefore, n ths work the requred GenCos GENCO = DPM DISCO (6) Fnally, for ths work, the controllers gans as well as the frequency bases are set to be equal for both areas..1 Control Strateges under Study The conventonal automatc generaton controller found mostly n lterature has a lnear ntegral only control strategy of the followng form and also sometmes researchers use contnuous tme models whch are completely napproprate,.e. u K e t dt (7) I

5 154 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp In ths work, for achevng the basc objectves of load-frequency control problem,.e., zero steady-state error n frequency and telne power, and also for completeness purposes snce our goal s the overall conventonal controllers performance evaluaton, the dscrete type of ntegral (I), proportonal plus ntegral (PI) and proportonal plus ntegral plus dervatve (PID) controller s used (taken from Smulnk/Matlab lbrary) as already shown n Fgure. 5. Parameter tunng and n depth dscusson of such type of controllers can be found n Wu and Huang (1997). In our case, the control law for the th area (=1,) s gven by de u KPe t KI e tdt K D dt whch when mplemented n the Smulnk/Matlab envronment takes the form Tsm u K e kts K e kts t K P I D t e kts t (8) (9) where K I, K P and K D are the gans of the PID controllers (K P, K D or K D are set to zero when a I or a PI s needed respectvely), T s s the samplng tme, T sm s the total smulaton tme and k=1,,..,t sm /T s. In ths study, the optmum values of these gans along wth the bas factor B whch mnmze a whole set of dfferent performance ndces are easly and accurately computed usng a genetc algorthm. In a typcal run of the GA, an ntal populaton s referred to as the th generaton. Each ndvdual n the ntal populaton has an assocated performance ndex value. Usng the performance ndex nformaton, the GA then produces a new populaton. The applcaton of a GA nvolves repettvely performng two steps: the calculaton of the performance ndex for each of the ndvduals n the current populaton. To do ths, the system must be smulated to obtan the value of the performance ndex; the GA then produces the next generaton of ndvduals usng the reproducton, crossover and mutaton operators. These two steps are repeated from generaton to generaton untl the populaton has converged, producng the optmum parameters. A flowchart of the GA optmzaton procedure s gven n Fgure Genetc Algorthm Overvew and Implementaton Aspects Genetc algorthms (GA), a way to search randomly for the best answers to tough problems were frst ntroduced by Holland (1975). Over the past years, t s becomng mportant to solve a wde range of search, optmzaton and machne learnng problems. A GA s an teratve procedure whch mantans a constant sze populaton of canddate solutons. The algorthm begns wth a randomly selected populaton of functon nputs represented by strng of bts. Durng each teraton step, called a generaton, the structures n the current populaton are evaluated and on the bass of ths evaluaton, a new populaton of canddate soluton s formed. That s GA uses the current populaton of strng to create a new populaton such that the strngs n the new populaton are on average better than those n the current populaton. The dea s to use the best elements from the current populaton to help form the new populaton. If ths s done correctly, then the new populaton wll on average be better than the old populaton. Three basc processes, namely selecton, matng (or crossover) and mutaton are used to make the transton from one populaton generaton to the next. In addton, GA works wth a codng of parameters rather than the parameters themselves, thereby freeng tself of the lmtatons (e.g. contnuty and dervatve exstence) of conventonal technques such as gradent methods (Wu and Huang, 1997). The smplfed genetc algorthm cycle based on the above s shown n Fgure 6, whle the man pseudo-code mplemented n MATLAB envronment for ths work s depcted n Fgure 7. End Convergence? Start Intal Populaton Evaluaton Crossover Selecton Mutaton Fgure 6. Smplfed flowchart of a typcal GA.

6 155 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp GA's Processes The above three steps are repeated to create each new generaton. And t contnues n ths fashon untl some stoppng condton s reached (e.g. maxmum number of generatons or resultng new populaton not mprovng fast enough). Selecton: Ths s the frst step of the three genetc operatons. It determnes whch strngs n the current populaton wll be used to create the next generaton. Ths s done by usng a based random selecton methodology. That s, parents are randomly selected from the current populaton n such a way that the "best" strngs n the populaton have the greatest chance of beng selected. There are many ways to do ths. One wde known technque s roulette wheel parent selecton (Grefenstette, 1986) whch s also used here. Crossover: Ths s a randomzed yet structured recombnaton operaton. Smple crossover may proceed n two steps. Frst, the newly reproduced strngs n the matng pool are mated at random. Second, crossover of each par of strngs s done as follows: () an nteger poston p along a strng s selected at random n the ntervals [1, L-1], where L s the strng length and () two new strngs are created by swappng all characters between poston 1 and p nclusvely. 1) Intalze Matlab/Smulnk Workspace ) Set Power System Model Parameters (Governors, Reheaters, Turbnes, Droops, PI Controllers, Te Lne, Gans) 3) Set Deregulated Envronment Parameters (Te Lnes, Demands, Area Partcpaton Factors, Dsco Partcpaton Matrx, Contracts) 4) Set Genetc Algorthm Parameters (pop sze, no generatons, crossover and mutaton values, other varables) 5) gen=1 6) Intalze populaton (Consstng of chromosomes pertanng controller values and frequency bases) 7) Set controller gans and freq. bases to system model 8) Smulaton of the system 9) Assgn ftness-value to entre populaton 1) Keep best values 11) gen=gen+1 whle (gen < Max.Generatons) or (Converge) 1) Select ndvduals for breedng 13) Recombne selected ndvduals (crossover) 14) Perform mutaton on offsprng 15) Form new populaton 16) Set controller gans and freq. bases to system model 17) Smulaton of the system 18) Evaluate new populaton 19) Keep best values End Whle Fgure 7. Genetc algorthm pseudo-code as appled to ths work. Mutaton: Reproducton and crossover effectvely search and recombne the exstng chromosomes. However, they do not create any new genetc materal n the populaton. Mutaton s capable of overcomng ths shortcomng. It s an occasonal random alteraton of a strng poston. In the bnary strng representaton, ths smply means changng a 1 to or vce versa. Ths random mutaton provdes background varaton and occasonally ntroduces benefcal materals nto the populaton. 3. GA's Parameters Selecton Genetc parameters, namely populaton sze, crossover rate (P c ) and mutaton rate (P m ), are the enttes that help to tune the performance of the GAs. The selecton of values for these parameters plays an mportant role n obtanng an optmal soluton. There are no determnstc rules to decde these values, but there are some general gudelnes whch can be followed to arrve at optmal values for these parameters and whch can be found n Holland (1975). Control Parameters Selected: Frst of all, the effect of populaton szes for dfferent test cases was observed. Dfferent populatons (, 5, 6, 8, and 1) were consdered and t has been observed that the populaton sze 5 or even 4 was satsfactory. After selectng the populaton sze, the effect of mutaton and crossover probabltes was examned. It has been found that sutable combnaton of mutaton and crossover probabltes gvng the best performances vares wth test cases. Dfferent combnatons of mutaton probabltes (.1,.1,.5,.1) and crossover probabltes (.6,.8,.9, and 1.) were tested and t was found that P c =1. and P m =.5 gve the best performance for all the test cases. Encodng: The desgn varables are mapped onto a fxed-length bnary dgt strng whch s constructed over the bnary alphabet {, 1}, and s concatenated head-to-tal to form one long strng called a chromosome. That s, every strng contans all desgn varables. Each desgn varable s represented by a λ-bt strng. We have to determne the value of λ. It s shown by Ln and Hajela (199) that: u l x x log where x u =upper bound on x; x l =lower bounds on x; ε=the resoluton. For example, f ε=.1, x u =6., x l =., then λ 1. Decodng: The physcal value of desgn varable x s computed from the followng equaton (1) u l l x x x x I (11) 1

7 156 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp For example, f ε=.1, x u =6., x l =. and λ=1, then the bt strng 11 s decoded to I=49 and thus x= Durng the optmzaton process upper and lower bounds of all the controllers gan settngs and bas factors were selected as [-5, 5] respectvely, and the bt sze (gene length) of each varable as (.e. λ=). 3.3 Ftness-Objectve Functon and Performance Indces under Consderaton In GAs, the value of ftness represents the performance whch s used to rank the strng, and the rankng s then used to determne how to allocate reproductve opportuntes. Ths means that ndvduals wth a hgher ftness value wll have a hgher opportunty of beng selected as a parent. Thus, ftness s some measure of goodness to be maxmzed. The ftness functon s essentally the objectve functon for the problem. In unconstraned maxmzaton problem, the objectve functon can be drectly adopted as the ftness functon F=J where F s the ftness functon and J s the objectve functon. The unconstraned mnmzaton problem accordng to the equaton F=K/J where K s a postve constant multpler. To maxmze the ftness functon s the same as mnmzng the objectve functon. The transent performance of the two area nterconnected power system n the deregulated envronment wth respect to the control of the frequency and te lne powers obvously depends on the value of the controllers' gans and the frequency bas. The optmum parameter values of the classcal AGC have been obtaned n the lterature (usng ntegral or proportonal-plus-ntegral) by mnmzng the popular ntegral of the squared error crteron (ISE) (Abdel-Magd and Dawoud, 1997). Ths crteron has been used because of the ease of computng the ntegral both analytcally and expermentally. A characterstc of the ISE crteron s that t weghts large errors heavly and small errors lghtly and t s not very selectve. A system desgned by ths crteron tends to show a rapd decrease n a large ntal error. Hence the response s fast, oscllatory and the system has poor relatve stablty. In ths work, we nvestgate the optmum adjustment of the load frequency controllers by extendng ths ssue, by ncorporatng a set of performance ndces whch are varous functons of error and tme. In ths way, someone can observe the varous performances that such a knd of power system mght have when a dfferent performance ndex s used. It should be noted that to the extent of the authors' knowledge, ths knd of optmzaton has not been done n the lterature before. Fnally, t s envsaged that the synthess procedure hghlghted n ths paper could be of practcal sgnfcance for tunng those AGC parameters for smlar power systems. The ndces adopted here nclude: The ntegral of the square of the error crteron (ISE) whch s gven by: ISE e t dt (1) The ntegral of tme-multpled absolute value of the error crteron (ITAE) whch s gven by: ITAE t e t dt (13) Ths crteron penalzes long duraton transents and s much more selectve than the ISE. A system desgned by use of ths crteron exhbts small overshoot and well damped oscllatons. The ntegral of tme-multpled square of the error crteron (ITSE) whch s gven by: ITSE te t dt (14) Ths crteron weghts large ntal error lghtly, whle errors occurrng late n the transent response are penalzed heavly. Ths crteron has a better selectvty than the ISE. (d) The ntegral of squared tme-multpled absolute value of the error crteron () whch s gven by: t e t dt (15) (e) The ntegral of squared tme-multpled square of the error crteron () whch s gven by: t e t dt (16) Even though performance ndces through (e) have not been appled to any great extend n practce due to the ncreased dffculty n handlng them, they are consdered here. If the power system model of Fgure 1 s taken nto account and also, a dscrete tme control s performed, Eqs. (1)-(16), are then translated nto the followng forms respectvely Tsm 1 te 1 J ISE P f f t (17) Tsm te 1 J ITAE t P f f t (18)

8 157 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Tsm 3 te 1 J ITSE t P f f t (19) Tsm 4 te 1 J t P f f t () Tsm 5 te 1 J t P f f t (1) where J m (m=1..5) s the objectve functon as descrbed above and α, β are penalty coeffcents whch n our case are set to unty. To compute the optmum parameter values, unt step load changes are assumed n one or both areas and the performance ndex s mnmzed usng the GA. In the next Secton, the optmum values of the parameters K P, K I, K D and B resultng from mnmzng the fve dfferent performance ndces are presented. Snce each performance ndex gves values n dfferent orders of magntude, a common performance measure must be also adopted for comparson purposes between them. Thus, the ntegral or absolute error (IAE) s ntroduced here whch gves the area under each curve through tme and can be expressed as 4. Case Studes Tsm 1 J IAE P f f t () c te The proposed controllers are appled for each control area of the restructured power system as shown n Fgure 3. To llustrate robustness of the proposed control strateges aganst parametrc uncertantes and contract varatons, smulatons are carred out for three cases of possble contracts under varous operatng condtons and load demands (Karnavas, 5). 4.1 Case 1: Exclusve Case: The GenCos n each area partcpate equally n AGC;.e., all four apf values are equal to.5. Contracts are made only between DsCos n area I and GenCos n area I, to purchase.1 pumw for each of them. In other words the load change occurs only n area 1. The followng data are applcable for ths case: DPM, DISCO pumw (3) Each area s load s the sum of the local DsCos demand,.e. ΔPL 1 =. and therefore ΔPL =. 4. Case : Normal Case: All the DsCos contract wth the GenCos for power as per the followng DPM: DPM, DISCO pumw (4) It s assumed that each DsCo demands.1 pumw power from GenCos as defned by cpfs n DPM matrx and each GenCo partcpates n AGC by followng apfs: apf 1 =.75, apf =.5, apf 3 =.5, apf 4 =.5. Also, ΔPL 1 =.15 and therefore ΔPL = Case 3: Contract Volaton Case: It may happen that a DsCo volates a contract by demandng more power than that specfed n the contract. Ths excess power s not contracted out to any GenCo. Ths un-contracted power must be suppled by the GenCos n the same area as the DsCo. It must be reflected as a local load of the area but not as the contract demand. So, consder Case agan wth a modfcaton that DsCo1 demands.1 pumw of excess power, whch s reflected now n ΔPL 1 whch now s set to ΔPL 1 =.5.

9 158 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Smulaton Results and Dscusson The tme responses of the system are smulated and the sgnals are sampled at 1Hz. These responses are presented n Fgures 8-1 for the I-type controller, n Fgures for the PI-type controller and n Fgures for the three cases respectvely. All these results show the effects of the load change n: the areas frequency devatons, the generated powers of the varous GenCos followng the step change n the load demands of the DsCos and the actual power flow on the te lne (e.g. n a drecton from area I to area II for Case 1). Vsually, the GA-tuned system has qute fast frequency response. The frequency devaton n each area goes to zero n the steady state. Also, n the steady state, generaton of a GenCo matches the demand of the DsCos n contract wth t. Generally speakng, t can be sad that no matter the type of controller adopted, each one seem to succeed to come to steady state qute easly and also satsfactorly (but of course they pertan small oscllatons around the nomnal value.e. Δf=). By nspecton of the aforementoned fgures t s also clear that, when PID-type controllers are used, they act too fast to the generator nputs (ths s not desrable due to the wear and tear of the machnes) and also exhbt very fast oscllatons. Thus, I-type or PI-type controllers seem to be the better choce for the system under study especally when they are to be tuned properly. Apart from that, n all cases, an acceptable overshoot and settlng tme on frequency devaton sgnal n each control area s mantaned and also, a reasonable lmt on the control acton sgnal, n the vewpont of change speed and ampltude, s assured. Tables 1-3 gve the optmum controller gan (K I ) for the I-type controller, Tables 4-6 gve the optmum controller gans (K P, K I ) for the PI-type controller and Tables 7-9 gve the optmum controller gans (K P, K I, K D ) for the PID-type controller. Also n these Tables, the values of the frequency bases B for the two areas obtaned by the applcaton of the GA are gven along wth the correspondng objectve functon value (J m ) and the values of the common (comparatve) performance measure (J c ). It s clearly shown that for dfferent cases, dfferent performance ndces gve the best optmzaton parameters values. The latter proves that when research work s done n such knd of power system models, several performance ndces must be examned thoroughly before extractng valuable nformaton about the correct system controller s tunng. Another nterestng thng to observe from Fgures 8-16 (n most cases and excludng the PID-type control) s that the quanttes that are nvolved to the objectve functon (.e. Δf and ΔP te ), have the fastest response when the PI-type controllers are appled, but the rest quanttes (.e. the generated powers of the GenCos) have the fastest response and wth less oscllatons when the I-type controllers are appled. Ths also leads to the concluson that the choce of the objectve functon s crucal and the behavor of the tuned system s drectly depended on t. Table 1. Optmum values for I-type controller gans, frequency bases and ftness functon obtaned by GA for Case 1. K I B J m J c Table. Optmum values for I-type controller gans, frequency bases and ftness functon obtaned by GA for Case. K I B J m J c Table 3. Optmum values for I-type controller gans, frequency bases and ftness functon obtaned by GA for Case 3. K I B J m J c Table 4. Optmum values for PI-type controller gans, frequency bases and ftness functon obtaned by GA for Case 1. K P K I B J m J c

10 159 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Table 5. Optmum values for PI-type controller gans, frequency bases and ftness functon obtaned by GA for Case. K P K I B J m J c Table 6. Optmum values for PI-type controller gans, frequency bases and ftness functon obtaned by GA for Case 3. K P K I B J m J c Table 7. Optmum values for PID-type controller gans, frequency bases and ftness functon obtaned by GA for Case 1. K P K I K D B J m J c Table 8. Optmum values for PID-type controller gans, frequency bases and ftness functon obtaned by GA for Case. K P K I K D B J m J c Table 9. Optmum values for PID-type controller gans, frequency bases and ftness functon obtaned by GA for Case 3. K P K I K D B J m J c Conclusons The mportant role of AGC wll contnue n restructured electrcty markets, but wth modfcatons. Blateral contracts can exst between DsCos n one control area and GenCos n other control areas. The use of a DPM facltates the smulaton of these blateral contracts. So, the modfed AGC scheme n a deregulated envronment ncludes contract data and measurements along wth the varous possble types of contracts combnatons. In ths new restructured envronment, GenCos sell power to varous DsCos at compettve prces, and the mnmzaton of the total cost n ths open market, s one of the most mportant aspects. In ths context, the tunng of area controllers n an AGC deregulated system s dscussed and appled. It s evdent that n ths tunng process, GAs are a valuable tool and provde qute easly the best answers for such a knd of problems. Controller gans and frequency bases are obtaned for I-type, PI-type and PID-type controllers for a two-area nterconnected restructured thermal power system wth reheat turbnes. Several performance ndces are consdered. These nclude n addton to the popular ntegral square of the error (ISE), the ntegral of tme-multpled absolute value of the error (ITAE), the ntegral of tme-multpled square of the error (ITSE), the ntegral of squared tme-multpled absolute value of the error (), and the ntegral of squared tmemultpled square of the error (). For each performance ndex, dgtal smulatons of the system are carred out and

11 P te P te GenCoPower GenCoPower GenCo1Power GenCo1Power f f f 1 f Fgure 8. Transent system s responses for Case 1 wth I-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power Fgure 9. Transent system s responses for Case wth I-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power.

12 P te P te GenCoPower GenCoPower GenCo1Power GenCo1Power f f f 1 f Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Fgure 1. Transent system s responses for Case 3 wth I-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power Fgure 11. Transent system s responses for Case 1 wth PI-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power.

13 P te P te GenCoPower GenCoPower GenCo1Power GenCo1Power f f f 1 f 1 16 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Fgure 1. Transent system s responses for Case wth PI-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power Fgure 13. Transent system s responses for Case 3 wth PI-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power.

14 P te P te GenCoPower GenCoPower GenCo1Power GenCo1Power f f f 1 f Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp x x Fgure 14. Transent system s responses for Case 1 wth PID-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power Fgure 15. Transent system s responses for Case wth PID-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power.

15 P te GenCoPower GenCo1Power f f Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp x optmzaton of the parameters of the AGC systems s acheved n a smple and elegant manner through the effectve applcaton of genetc algorthms. It s clear that the dynamc performance of the system, usng the optmal parameters, s resultng from the mnmzaton of a dfferent performance ndex (and not only the ISE usually used n lterature). It s also seen that the choce of the objectve functon s mportant and affects the behavor of the system. Ths way, the lack of poor dampng and settlng tme (relatve to the other ndces) as well as the mprovement of the transent error n both the frequency and te-lne power, can be assured. Also, the results obtaned ndcate the approprateness of I or PI over the PID strategy. Further work should nclude mult area systems, new controller structures as well as dfferent power system characterstcs.e. hydro and desel unts for the GenCos. Nomenclature f, Δf power system frequency, devaton of P r area s nomnal nstalled capacty ΔP L area s load dsturbance ΔP te nterchange area s te lne error P tj turbne s block output sgnal of generaton company j P gj governor s block output sgnal of generaton company j K ps, T ps power system s block gan and tme constant of area K tj, T tj turbne s block gan and tme constant of generaton company j K gj, T gj governor s block gan and tme constant of generaton company j K rj, T rj reheater s block gan and tme constant of generaton company j R j governor droop parameter of generaton company j B area s frequency bas parameter cpf contract partcpaton factor apf area partcpaton factor u area s controller s output sgnal K P, K I, K D proportonal, ntegral and dervatve gans of a PID structure controller J performance ndex F ftness functon of the genetc algorthm T s, Δt smulaton and samplng tme α, β weght values used by the ftness functon P c genetc algorthm s crossover rate P m genetc algorthm s mutaton rate λ chromosome s bt length x u, x l genetc algorthm varable upper and lower bounds z -1 dscrete tme system delay Fgure 16. Transent system s responses for Case 3 wth PID-type control w.r.t. the fve performance ndces: frequency devatons, Te lne power, GenCos generated power.

16 165 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Appendx A: Power System Data P r1 =P r =MW, f o =6Hz, K ps1 =K ps =1Hz/puMW, T ps1 =T ps =sec, K t1 =K t =K t3 =K t4 =.5, T t1 =T t =T t3 =T t4 =.3sec, K g1 =K g =K g3 =K g4 =1, T g1 =T g =T g3 =T g4 =.8sec, K r1 =K r =K r3 =K r4 =.5, T r1 =T r =T r3 =T r4 =1.sec, R 1 =R =R 3 =R 4 =.4Hz/puMW, T 1 =.545puMW, a 11 =a 1 =-1, B o =.45puMW/Hz. Appendx B: Genetc Algorthm Parameters Parameter Value Maxmum no of generatons * 3 No of populaton sze 5 Unform crossover Yes Crossover probablty 1. Eltsm Yes Mutaton probablty.5 Creep mutatons Yes Creep mutaton probablty. References Abdel-Magd Y.L., Dawoud M.M., Optmal AGC tunng wth genetc algorthms, Electrc Power Systems Research, Vol. 38, pp Adtya S.K., Das D., 3. Desgn of load frequency controllers usng genetc algorthms for two area nterconnected hydro power system, Electrc Power Components and Systems, Vol. 31, No. 1, pp A-Hamouz Z.M., Abdel-Magd Y.L., Varable structure load frequency controller for multarea power systems, Int. Journal of Electrc Power and Energy Systems, Vol. 15, No. 5, pp Bevran H., Mtan Y., and Tsuj K., 4. Robust decentralzed AGC n a restructured power system. Energy Converson & Management, Vol. 45, pp Chrste R., Bose A., Load-frequency control ssues n power systems operaton after deregulaton. IEEE Trans. on Power Systems, Vol. 11, pp Chrste R.D., Wollenberg B.F., and Wangensteen I.,. Transmsson management n the deregulated envronment. Proc. IEEE Specal Issue on The Technology of Power System Competton, Vol. 88, No., pp Cohn N., Control of generaton and power flow on nterconnected systems. Wley, New York. Delfno B., Fornar F., and Massucco S.,. Load-frequency control and nadvertent nterchange evaluaton n restructured power systems. Proc. IEE Gen. Trans. Dstr., Vol. 149, No. 5, pp Demroren A., Zeynelgl H.L., 7. GA applcaton to optmzaton of AGC n three-area power system after deregulaton. Internatonal Journal of Electrcal Power & Energy Systems, Vol. 9, No. 3, pp Donde V., Pa M.A., and Hskens I.A., 1. Smulaton and optmzaton n an AGC system after deregulaton. IEEE Trans. on Power Systems, Vol. 16, No. 3, pp Elgerd O.I., 197. Optmum megawatt-frequency control of mult-area electrc energy systems. IEEE Trans. on PAS, Vol. 89, No. 4, pp Flemng P.J., Fonseca C.M., Genetc algorthms n control systems engneerng, Research Report No. 47, Dept. of Automatc Control and Systems Engneerng, Unversty of Sheffeld, Sheffeld, UK. Grefenstette J.J., Optmzaton of control parameters for genetc algorthms. IEEE Trans. on System, Man and Cybernetcs, Vol. SMC-16, pp Holland J.H., Adaptaton n Nature and Artfcal Systems. Unversty of Mchgan Press. Ibraheem, Sngh O., Hasan N., 9. Genetc Algorthm Based Scheme for Optmzaton of AGC Gans of Interconnected Power System. Journal of Theoretcal and Appled Informaton Technology, Vol. 1, No. 1, pp Ilc M., Galana F., and Fnk L., Eds., Power Systems Restructurng: Engneerng & Economcs. Boston: Kluwer Academc Publshers. Karnavas Y.L., 5. On the Optmal Control of Interconnected Electrc Power Systems n a Re-Structured Envronment Usng Genetc Algorthms, WSEAS Transactons on Systems Journal, Vol. 4, No. 8, pp Karnavas Y.L., Papadopoulos D.P.,. AGC for autonomous power staton usng combned ntellgent technques. Int. J. Electrc Power Systems Research, Vol. 6, pp Kumar A., Malk O.P., and Hope G.S., Varable-structure-system control appled to AGC of an nterconnected power system. IEE Proc. Part C, Vol. 13, No. 1, pp Kumar J., Ng K.H., Sheble G., AGC smulator for prce-based operaton-part I: A model. IEEE Trans. on Power Systems, Vol. 1, No., pp Ln C. Hajela Y.P., 199. Genetc algorthms n optmzaton problems wth dscrete and nteger desgn varables. Engneerng Optmzaton, Vol. 19, No. 4, pp

17 166 Karnavas and Dedouss / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 1, pp Noble E., Bose A., and Tomsovc K.,. Blateral market for load followng ancllary servces. Proc. PES Summer Power Meetng, July 15-1, Seattle, WA. Pan C.T., Lan C.M., 5. An adaptve controller for power system load frequency control. IEEE Transactons on Power Systems, Vol. 4, No. 1, pp Shayegh H., Shayanfar H.A., Jall A. 6. Mult stage fuzzy PID power system automatc generaton controller n the deregulated envronment. Energy Converson and Management, Vol. 47, No. 18, pp Sheble G.B., Computatonal Aucton Mechansms for Restructured Power Industry Operaton. Boston: Kluwer Academc Publshers. Snha S.K., Prasad R., Patel R.N., 1. Automatc generaton control of restructured power systems wth combned ntellgent technques. Internatonal Journal of Bo-Inspred Computaton, Vol., No., pp Srnvasa R.C., Sva N.S, Sangameswara R.P., 8. AGC Tunng of TCPS Based Hydrothermal System under Open Market Scenaro wth Partcle Swarm Optmzaton, J. Electrcal Systems, Vol. 4, No., pp Wu C. J., Huang C.H., A Hybrd Method for Parameter Tunng of PID Controllers. Journal of Frankln Insttute, JFI-334B, pp Bographcal notes: Dr. Eng. Yanns L. Karnavas s Assstant Professor at the Department of Electrcal Engneerng, Technologcal Educatonal Insttuton of Crete, Heraklon, Crete, Hellas. He has engaged n teachng and research actvtes the last 15 years. Hs felds of expertse are the analyss and modelng of power systems and electrc machnes, the desgn and applcaton of varous types of controllers and artfcal ntellgence methods applcaton to them. Dr.Eng. Karnavas has publshed several papers n varous natonal, nternatonal journals and conferences as well as book chapters n nternatonal engneerng books. He has also partcpated n research projects as research leader or scentfc assocate. Konstantnos S. Dedouss s a graduate Electrcal Engneer from the Department of Electrcal Engneerng, Technologcal Educatonal Insttuton of Crete, Heraklon, Crete, Hellas. He has done extensve work on the feld of modelng of power systems wth varous types of generatng sources and also the feld of desgnng load frequency controllers for them. Presently, he s focusng on analyss of permanent magnet synchronous generators and ther mplementaton n power system studes. Receved November 9 Accepted March 1 Fnal acceptance n revsed form March 1