Dual Proportional Integral Controller of Two-Area Load Frequency Control Based Gravitational Search Algorithm

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1 TELKOMNIKA Inonesan Journal of Electrcal Engneerng Vol. 15, No. 1, July 2015, pp. 26 ~ 35 DOI: /telkomnka.v Dual Proportonal Integral Controller of Two-Area Loa Frequency Control Base Gravtatonal Search Algorthm M. Elss 1, M. Solman 2, M. A. S. Aboelela 3, W. Mansour 4 1,2,4 Electrcal Power an Machnes Department, Faculty of Engneerng (Shoubra), Benha Unversty, Caro, Egypt, 108 Shoubra St., B.O. Box 11241, Tel.: Electrcal Power an Machnes Department, Faculty of Engneerng, Caro Unversty, Gza, Egypt Corresponng author, e-mal: elssmahmou22@yahoo.com 1, msolman_28@yahoo.com 2, wagy_brahm2010@yahoo.com 3, magysafaa@yahoo.com 4 Abstract Gravtatonal Search Algorthm (GSA) has recently been explore to evelop a novel algorthm for strbute optmzaton an control. Ths paper proposes a ual Proportonal Integral (PI) controller of Loa Frequency Control (LFC) base GSA to enhance the ampng of os cllatons n a two-area power system. A two-area non-reheat thermal system s consere to be equppe wth ual PI controller. GSA s utlze to search for optmal controller parameters by mnmzng a tme-oman base obectve functon. The performance of the propose controller has been evaluate wth the performance of the conventonal PI controller, an PI controller tune by GSA n orer to emonstrate the superor effcency of the propose ual PI controller tune by GSA. Smulaton results emphass on the better performance of the optmze ual PI controller base on GSA n compare to optmze PI controller base on GSA an conventonal one over we range of operatng contons, an system parameters varatons. Keywor: gravtatonal search algorthm, loa frequency control, ual PI controller Copyrght 2015 Insttute of Avance Engneerng an Scence. All rghts reserve. 1. Introucton Frequency control, urng the loa an generaton mbalance, represents a very mperatve ssue for large-scale power systems. Automatc generaton control (AGC) plays a sgnfcant role n the power system by mantanng the scheule system frequency an te-lne power flow urng normal operatng contons an urng small perturbatons [1-3]. Ths functon of an AGC s always referre to as loa frequency control (LFC) as mentone by Kunur [2]. LFC s often consere as one of the frst an foremost large-scale, ecentralze, robust controllers n engneerng practce. LFC s accomplshe by two fferent control actons of the prmary spee control an supplementary spee control n an nterconnecte power system. In the lterature, some control strateges have been suggeste base on the conventonal lnear control theory. The conventonal PI controller s consere the most wely controller between varous types of loa frequency controllers. The PI controller s very smple for applcaton an gves better ynamc response, but ther performance eterorates when the complexty n the system ncreases [4]. The PI control strategy has slghtly smaller overshoot than ntegral control strategy but settlng tme for only ntegral control s less. The response wth the PI controller has more oscllatory than the ntegral controller [5]. Control system performance can be mprove by allowng the controller to swtch from one moe to another. For nstance, for certan lnear systems swtchng from a proportonal controller to ntegral controller n a feeback loop may prove a fast response an small overshoot [6]. Base upon the above-mentone facts, t s esrable to aopt a ual moe controller conclue both proportonal an ntegral controller. In [5] the rate of change of the error s use as swtchng crtera between proportonal an ntegral controller. The proportonal controller acts when rate of change of the error s suffcently large, whereas the ntegral controller woul be better one when the rate of change of the error s small. In [7-9] the error s use as swtchng crtera between proportonal an ntegral controller. The proportonal controller s use when the error s large, the ntegral Receve March 6, 2015; Revse May 14, 2015; Accepte Jun 2, 2015

2 TELKOMNIKA ISSN: controller acts when the error s small. The man problem whch faces ual moe controller n [5-9], t s the swtchng conton. Ths paper proposes to solve ths problem by make relaton between the swtchng conton an the summaton of sturbance on the system. If summaton of sturbance on the system ncrease the swtchng conton ncrease. In orer to get better performance from any controller, ts parameters nee goo optmzaton. The conventonal methos face some ffcultes to acheve ths purpose, such as complex mathematcal equatons for large systems. Several approaches such as optmal, Genetc Algorthm (GA), Partcle Swarm Optmzaton (PSO), Bacteral Foragng Optmzaton (BFO), etc., for the esgn an optmzaton of the LFC system, have been reporte n the lterature [10-21]. Moern optmal control concept for AGC esgns of nterconnecte power system was frstly presente by Elger an Fosha [10-11]. Genetc algorthms (GAs) have been extensvely consere for the esgn of AGC. Optmal ntegral gans an optmal PID control parameters have been compute by GAs technque for an nterconnecte, equal non-reheat an reheat type two generatng areas [12-13]. In [14] the Parameters of PID slng-moe use n LFC of mult area power systems wth nonlnear elements are optmze by GA. In [15], GA s use to compute the ecentralze control parameters to acheve an optmum operatng pont for a realstc system comprsng generaton rate constrant (GRC), ea ban, an tme elays. The use of partcle swarm optmzaton (PSO) for optmzng the parameters of AGC, where an ntegral controller an a proportonal-plus-ntegral controller, s reporte n [16]. In [17] the parameters of PI controller are esgne by PSO wth the new cost functon an compare ther results wth [16]. In [18], a robust PID controller base ICA use for LFC applcaton. The authors of [19-20] have propose bacteral foragng optmzaton algorthm (BFOA) for esgnng PI an PID-base loa frequency controller for two-area power system wth an wthout GRC. Applcaton of BFOA to optmze several mportant parameters n AGC of an nterconnecte three unequal area thermal systems such as the ntegral controller gans, governor spee regulaton, an the frequency bas parameters, has been reporte n [21]. In [22] a new optmzaton algorthm base on the law of gravty an mass nteractons s ntrouce. In the algorthm, the searcher agents are a collecton of masses whch work wth each other base on the Newtonan gravty an the laws of moton. Ths paper proposes the GSA for optmal tunng of ual PI controller n two area nterconnecte power system to amp power system oscllatons. The ual PI control esgn s formulate as an optmzaton problem an GSA s employe to search for optmal controller parameters by mnmzng a canate tme-oman base obectve functon. The consere obectve functon nvolves the ntegral tme multply the absolute error (ITAE) n the frequency an te lne power. The performance of the propose ual PI control-base GSA s evaluate by comparson wth PI-base GSA. Smulatons results on a two-area test system are presente to assure the superorty of the propose metho compare wth PI-base GSA an conventonal one. 2. Gravtatonal Search Algorthm Gravtatonal Search Algorthm (GSA) s a novel heurstc algorthm nspre by the Newtonan laws of gravty an moton [22]. In GSA, agents are consere as obects an ther performance s evaluate by ther masses. All these obects attract each other by the force of gravty an moves towar the obects wth a heaver mass. The heavy masses correspon to goo soluton, an ths guarantees the explotaton step of the algorthm. In GSA, each mass (agent) has four representatons: poston, nertal mass, actve gravtatonal mass an passve gravtatonal mass. The poston of the mass represent a soluton of the problem an t s gravtatonal an nerta masses are etermne usng a ftness functon. In other wors each mass presents a soluton an the algorthm s run by properly austng the gravtatonal an nerta masses. By lapse of tme t s prectable that masses be attracte by the heaver mass. Ths mass wll represent an optmum soluton n the search space. GSA s representng a small artfcal worl of masses obeyng the Newtonan laws of gravtaton an moton. Masses obey the followng laws [22-24] Law of Gravty Each agent attracts every other agent an the gravtatonal force between the two agent s rectly proportonal to the prouct of ther masses an nversely proportonal to the stance Dual Proportonal Integral Controller of Two-Area Loa Frequency Control Base (M. Elss)

3 28 ISSN: between them R. It has been conclue n the lterature that R proves better results than R^2 n all experment cases [22] Law of Moton The current velocty of any agent s equal the sum of the fracton of ts prevous velocty an the varaton n the velocty. Varaton n the velocty or acceleraton of any agent s equal to the force acte on the system ve by mass of nerta. For a system wth n agent (masses), the th poston of an agent X s efne by: X x x x for =1,2,,n (1) 1 n (,...,,...,) Where n s the space menson of the problem an, x s the represents the poston of th agent n the th menson. At a specfc tme t, the force actng on mass from mass s efne as followng: M p ()() t M a t F()(()()) G t x t x t R () t (2) Where M a s the actve gravtatonal mass relate to agent, M p s the passve gravtatonal mass relate to agent, G(t) s gravtatonal constant at tme t, ɛ s a small constant, an R (t) s the Euclan stance between two agents an : R ()(),() t x. t x t 2 (3) To gve a stochastc characterstc to algorthm, t s suppose that the total force that acts on mass n a menson be a ranomly weghte sum of th components of the forces exerte from other agents: N ()() 1, F t ra n F t, (4) Where ran s a ranom number n the nterval [0,1]. Hence, by the law of moton, the acceleraton of the mass at tme t, an n recton th, a () t, s gven as follows: a () t F () t, (5) M () t Where M s the nertal mass of th agent. Furthermore, the next velocty of an mass s consere as a fracton of ts current velocty ae to ts acceleraton.therefore, ts poston an ts velocty coul be calculate as follows: v ( t 1)()() ran v t a t, (6) x ( t 1)()( x 1) t v t, (7) Where ran s a unform ranom varable n the nterval [0,1]. The gravtatonal constant, G, s ntalze at the begnnng an wll be reuce wth tme to control the search upate. In other wors, G s a functon of the ntal value (G 0 ) an tme (t) as: G () t ( t /) T G 0 e. (8) TELKOMNIKA Vol. 15, No. 1, July 2015 : 26 35

4 TELKOMNIKA ISSN: Where α s a constant an T s the number of teraton. Gravtatonal an nerta masses are calculate by the ftness evaluaton. A heaver mass means a more effcent obect. Ths means that better obects have hgher attractons an walk more slowly. The gravtatonal an nertal masses of agents are upate by the followng equatons: M a M p M M, =1,2,.,N, (9) m () t ft ()() t w o r s t t b e s t ()() t w o r s t t, (10) M () t m () t, (11) N m () t 1 Where ft (t) present the ftness value of the agent at tme t, an, worst(t) an best(t) are efne as follows (for a mnmzaton problem): best() t mn() ft t, (12) 1,..., N w orst () t m ax() ft t. (13) 1,..., N It s to be note that for a maxmzaton problem, (12) an (13) are change to (14) an (15), respectvely: best() t max() ft t, (14) 1,..., N w orst () t m n() ft t 1,..., N (15) Fgure 1. Flow chart of GSA optmzaton approach To acheve a goo compromse between exploraton an explotaton, the number of obects s reuce wth lapse of (4) an therefore a set of obects wth bgger mass are use for applyng ther force to the other. The fferent steps of the propose algorthm are the followngs: a) Search space entfcaton. Dual Proportonal Integral Controller of Two-Area Loa Frequency Control Base (M. Elss)

5 30 ISSN: b) Ranom ntalzaton. c) Ftness evaluaton of obects. ) Upate G(t), best(t), worst(t) an M (t) for = 1,2,...,N. e) Calculaton of the total force. f) Calculaton of acceleraton an velocty. g) Upate the poston of the obects. h) Repeat steps c to g untl the stop crtera s acheve. The flow chart of propose optmzaton s shown n Fgure Dual PI Controller The control law employe epenng upon the magntue of the rate of change of the error sgnal. For (()) A C E t t U K A C E () t p (16) Where, ACE(t) s an error sgnal at a partcular nstant, ε s a small postve constant ncatng the specfe lmt of rate of change of the error sgnal, U the control sgnal to th area an K P s the proportonal gan. K N c 1 P L (17) Where K c s scalng factor, P L For (()) A C E t t U K A C E () t t s the sturbance n th area an N the total number of area. (18) Where K s the ntegral gan. Then f the parameters K p, K an K c are sutably selecte, one can ensure a hgh qualty transent response. By choosng a sutable value of K p, one makes sure that spee of the system s hgh. Whenever the rate of change of error falls wthn the specfe error boun (()) ACE t, the ntegrator starts accumulatng the error. But f the error excees the t boun the ntegrator resets to zero. The GSA s propose n ths paper to get the best value of K p, K an K c.the propose control scheme s shown n Fgure 2. Fgure 2. Block agram for the propose ual TELKOMNIKA Vol. 15, No. 1, July 2015 : 26 35

6 TELKOMNIKA ISSN: Two Area Power System A moel of controlle non-reheat thermal plants n two-area nterconnecte power system s shown n Fgure 3 where f s the system frequency (Hz), R s the regulaton constant (Hz/unt), T G s the spee governor tme constant (s), T T s the turbne tme constant (s) an T P s the power system tme constant (s), ACE s the area control error, P D s the loa eman change, P c s the change n spee changer poston, P G s the change n governor valve poston, K P s the power system gan, an P te s the change n te lne power. The overall system can be moele as a multvarable system n the followng form: x Ax Bu, (19) y x u cx f 1 P T1 P G1 P C1 P te f 2 P T 2 P G2 T T u u, y ACE ACE, P P T D1 D2 P C2 T (20) 5. Obectve Functon The performance nex whch selecte n ths paper can be efne by the Integral of Tme multply Absolute Error (ITAE) of the frequency evaton of both areas an te lne power. Accorngly, the obectve functon J s set to be: T s 0 J t f f P t 1 2 te (21) Where T s s the smulaton tme. Ths stuy focuses on optmal tunng of controllers for LFC usng GSA. The am of the optmzaton s to search for the optmum ual PI controller parameters settng that mprove the ampng characterstcs of the system uner all operatng contons an varous loas an fnally esgnng a low orer controller for easy mplementaton. Fgure 3. Two-area nterconnecte power system 6. Smulaton Results In ths secton fferent comparatve cases are examne to show the effectveness of the propose ICA metho for optmzng controller parameters of ual PI controller. Table 1 gves the optmum values of controller parameters for fferent methos. The PI controller parameters of conventonal controller ue to [19]. Dual Proportonal Integral Controller of Two-Area Loa Frequency Control Base (M. Elss)

7 32 ISSN: Table 1. Controller Parameters an Obectve Functon (J) Conventonal GSA-PI Dual PI PI Controller Parameters K p= , K I = K p= , K I = K p = , K I = , K c= J Step Increase n Deman of the Frst Area ( P D1 ) In ths case, a 0.1 step ncrease n eman of the frst area ( P D1 ) s apple (nomnal test case). The change n frequency of the frst area f 1, the change n frequency of the secon area f 2, an change n te-lne power of the close loop system are shown n Fgure 4-6. Remarkably, the response wth conventonal PI controller has hgh settlng tme an unesrable oscllatons. Also compare wth PI-base GSA the propose metho s nee more effcent n mprovng the ampng characterstc of power system. Fgure 4. Change n f 1 for 0.1p.u step ncrement n P D1 Fgure 5. Change n f 2 for 0.1p.u step ncrement n P D1 Fgure 6. Change n P te for 0.1p.u step ncrement n P D1 TELKOMNIKA Vol. 15, No. 1, July 2015 : 26 35

8 TELKOMNIKA ISSN: Step Increase n Deman of the Secon Area ( P D2 ) In ths case, a 0.1 step ncrease s apple as a change of eman n the secon area ( P D2 ). The change n frequency of the frst area f 1, the change n frequency of the secon area f 2 an change n te-lne power of the close loop system are shown n Fgure 7-9. From these Fgures t can be seen that oscllatons are sappear n the presence of the propose controller. Moreover, the propose metho outperforms an outlasts PI-base GSA n ampng oscllatons effectvely an reucng settlng tme. Hence compare to the conventonal controller, an PI-base GSA, ual PI base GSA greatly enhances the system stablty an mproves the ampng characterstcs of power system. Fgure 7. Change n f 1 for 0.1p.u step ncrement n P D2 Fgure 8. Change n f 2 for 0.1p.u step ncrement n P D2 Fgure 9. Change n P te for 0.1p.u step ncrement n P D Step Increase n Deman of the Frst an Secon Area Smultaneously In ths case, a 10% step ncrease n eman of the frst area ( P D1 ) an secon area ( P D2 ) smultaneously are apple. It s clear from Fgure 10 that the propose metho has a smaller settlng tme an system response s quckly rven back to zero compare wth conventonal controller an PI-base GSA In aton, the potental an superorty of the propose metho over the conventonal, an PI-base GSA s emonstrate. Dual Proportonal Integral Controller of Two-Area Loa Frequency Control Base (M. Elss)

9 34 ISSN: Fgure 10. Change n f 1 for 0.1p.u step ncrement n P D1 an P D Parameter Varaton A parameter varaton test s also apple to valate the robustness of the propose controller. Fgsure show the response of frequency of frst area wth varaton n T 12. It s clear that the system stable wth the propose controller. Fgure 11. Change n f 1 ue to +50% ncrease n T 12 Fgure 12. Change n f 1 ue to -50% ecrease n T Concluson Ths paper presents the applcaton of the GSA algorthm as a new artfcal ntellgence technque n orer to optmze the AGC n a two-area nterconnecte power system. GSA algorthm s propose to tune the parameters of ual PI controller. A two-area power system s consere to emonstrate the propose metho. Smulaton results emphass that the esgne ual PI-base GSA s robust n ts operaton an gves a superb ampng performance for frequency an te lne power evaton compare to conventonal PI controller, an PI-base GSA. Beses the smple archtecture of the propose controller t has the potentalty of mplementaton n real tme envronment. TELKOMNIKA Vol. 15, No. 1, July 2015 : 26 35

10 TELKOMNIKA ISSN: References [1] P Kunur. Power system stablty an control. McGraw-Hll [2] H Saaat. Power system analyss. Tata Mcgraw-Hll [3] OI Elgar. Electrcal Energy System theory: an Introucton. New Delh: McGraw-Hll [4] Prakash, Surya, SK Snha. Loa frequency control of three area nterconnecte hyro-thermal reheat power system usng artfcal ntellgence an PI controllers. Internatonal Journal of Engneerng, Scence an Technology. 2012; 4(1): [5] C Kalyan. Desgn of ual moe PI controller for loa frequency control. Internatonal Journal of Emergng Electrc Power Systems. 2010; 11(4): [6] S Tarq. Perspectves n Control Engneerng: Technologes, Applcatons, an New Drectons. Wley- IEEE Press [7] MOP Ashok Kumar, GS Hope. A loa frequency control algorthm base on a generalze approach. Power Systems, IEEE Transactons. 1988; 3(2): [8] M R, M Mohame Thameem Ansar. Loa frequency control usng Bat nspre algorthm base ual moe gan scheulng of PI controllers for nterconnecte power system. Internatonal Journal of Electrcal Power & Energy Systems. 2015; 64: [9] S, V Raasekaran. Desgn of ecentralze base ual moe controller for loa frequency control of an nterconnecte power system wth AC/DC te lnes. IPEC, 2010 Conference Proceengs, IEEE [10] OI Elger, CE Fosha. Optmum megawatt-frequency control of multarea electrc energy systems. IEEE Trans. Power App. Syst. 1970; 89(4): [11] CE Fosha, OI Elger. The megawatt-frequency control problem-a new approach va optmal control theory. IEEE Trans. Power App. Syst. 1970; 89(4): [12] SP Ghoshal, SK Goswam. Applcaton of GA base optmal ntegral gans n fuzzy base actve power-frequency control of nonreheat an reheat thermal generatng systems. Elect. Power Syst. Res. 2003; 67: [13] SP Ghoshal. Applcaton of GA/GA-SA base fuzzy automatc generaton control of a mult-area thermal generatng system. Elect. Power Syst. Res. 2004; 70: [14] L Pnkag, Z Hengun, L Yuyun. Genetc algorthm optmzaton for AGC of mult-area power systems. Proc. of IEEE Regon 10 conference on computers, communcatons, control an power engneerng (TENCON 02). 2002: [15] H Golpra, H Bevran. Applcaton of GA optmzaton for automatc generaton control esgn n an nterconnecte power system. Energy Converson an Management. 2011; 52: [16] YL Abel-Mag, MA Abo. AGC tunng of nterconnecte reheat thermal systems wth partcle swarm optmzaton. Proc. of the th IEEE nternatonal conference on electroncs, crcuts an systems. 2003; 1: [17] H Goze, MC Taplamacoglu, I Kocaarslan, MA Senol. Partcle swarm optmzaton base PI-controller esgn to loa frequency control of a two area reheat thermal power system. J Therm Sc Technol. 2010; 30(1): [18] H Shaban, B Vah, M Ebrahmpour. A robust PID controller base on mperalst compettve algorthm for loa-frequency control of power systems. ISA Trans. 2013; 52(1): [19] ES Al, SM Ab-Elazm. Bactera foragng optmzaton algorthm base loa frequency controller for nterconnecte power system. Int. J Electr. Power Energy Syst. 2011; 33(3): [20] ES Al, SM Ab-Elazm. BFOA base esgn of PID controller for two area Loa Frequency Control wth nonlneartes. Electrcal Power an Energy Systems. 2013; 51: [21] J Nanaa, S Mshra, LC Saka. Maen applcaton of Bacteral foragng-base optmzaton technque n mult-area automatc generaton control. IEEE Trans. Power Syst. 2009; 24(2): [22] R Esmat, Hossen Nezamaba-Pour, Sae Saryaz. GSA: a gravtatonal search algorthm. Informaton scences. 2009; 179(13): [23] R Esmat, Hossen Nezamaba-Pour, Sae Saryaz. Flter moelng usng gravtatonal search algorthm. Engneerng Applcatons of Artfcal Intellgence. 2011; 24(1): [24] P Purwoharono, et al. Optmal Placement an Szng of Thyrstor-controlle-seres-capactor usng Gravtatonal Search Algorthm. TELKOMNIKA (Telecommuncaton Computng Electroncs an Control). 2012; 10(4): Dual Proportonal Integral Controller of Two-Area Loa Frequency Control Base (M. Elss)