Multi-area Load Frequency Control using IP Controller Tuned by Particle Swarm Optimization

Transcription

1 esearch Journal of Applied Sciences, Engineering and echnology (): 96-, ISSN: -767 axwell Scienific Organizaion, Submied: July, Acceped: Sepember 8, Published: ecember 6, uli-area Load Frequency Conrol using IP Conroller uned by Paricle Swarm Opimizaion Sayed ojaba Shirvani Boroujeni, Babak Keyvani Boroujeni, osafa Abdollahi and Hamideh elafkar eparmen of Elecrical Engineering, Boroujen Branch, Islamic Azad Universiy, Boroujen, Iran Absrac: In his sudy an opimal load frequency conroller for muli area elecric power sysems is presened. In muli area elecric power sysems if a large load is suddenly conneced (or disconneced) o he sysem, or if a generaing uni is suddenly disconneced by he proecion equipmen, here will be a long-erm disorion in he power balance beween ha delivered by he urbines and ha consumed by he loads. his imbalance is iniially covered from he kineic energy of roaing roors of urbines, generaors and moors and, as a resul, he frequency in he sysem will change. herefore he Load Frequency Conrol (LFC) problem is one of he mos imporan subjecs in he elecric power sysem operaion and conrol. In pracical sysems, he convenional PI ype conrollers are carried ou for LFC. In order o overcome he drawbacks of he convenional PI conrollers, numerous echniques have been proposed in lieraures. In his paper a IP ype conroller is considered for LFC problem. he parameers of he proposed IP conroller are uned using Paricle Swarm Opimizaion (PSO) mehod. A muli area elecric power sysem wih a wide range of parameric uncerainies is given o illusrae proposed mehod. o show effeciveness of he proposed mehod, a PI ype conroller opimized by PSO is incorporaed in order o comparison wih he proposed IP conroller. he simulaion resuls on a muli area elecric power sysem emphasis on he viabiliy and feasibiliy of he proposed mehod in LFC problem. Key words: IP conroller, load frequency conrol, paricle swarm opimizaion, muli area elecric power sysem INOUCION For large scale elecric power sysems wih inerconneced areas, Load Frequency Conrol (LFC) is imporan o keep he sysem frequency and he iner-area ie power as near o he scheduled values as possible. he inpu mechanical power o he generaors is used o conrol he frequency of oupu elecrical power and o mainain he power exchange beween he areas as scheduled. A well designed and operaed power sysem mus cope wih changes in he load and wih sysem disurbances, and i should provide accepable high level of power qualiy while mainaining boh volage and frequency wihin olerable limis. any conrol sraegies for Load Frequency Conrol in elecric power sysems have been proposed by researchers over he pas decades. his exensive research is due o fac ha LFC consiues an imporan funcion of power sysem operaion where he main objecive is o regulae he oupu power of each generaor a prescribed levels while keeping he frequency flucuaions wihin pre-specifies limis. A unified uning of PI load frequency conroller for power sysems via inernal mode conrol has been proposed by an (). In his paper he uning mehod is based on he wo-egree-of-freedom (F) inernal model conrol (IC) design mehod and a PI approximaion procedure. A new discree-ime sliding mode conroller for load-frequency conrol in areas conrol of a power sysem has been presened by Vrdoljak e al. (). In his sudy full-sae feedback is applied for LFC no only in conrol areas wih hermal power plans bu also in conrol areas wih hydro power plans, in spie of heir non minimum phase behaviors. o enable full-sae feedback, a sae esimaion mehod based on fas sampling of measured oupu variables has been applied. he applicaions of arificial neural nework, geneic algorihms and opimal conrol o LFC have been repored by Kocaarslan and Cam (5), erkpreedapong e al. () and Liu e al. (). An adapive decenralized load frequency conrol of muliarea power sysems has been presened by Zribi e al. (5). Also he applicaion of robus conrol mehods for load frequency conrol problem has been presened by Shayeghi e al. (7) and aher and Hemai (8). his sudy deals wih a design mehod for LFC in a muli area elecric power sysem using a IP ype conroller whose parameers are uned using PSO. In order o show effeciveness of he proposed mehod, his IP conroller is Corresponding Auhor: Sayed ojaba Shirvani Boroujeni, eparmen of Elecrical Engineering, Boroujen Branch, Islamic Azad Universiy, Boroujen, Iran, ell.: ; Fax

2 es. J. Appl. Sci. Eng. echnol., (): 96-, Fig. : Four-area elecric power sysem wih inerconnecions Fig. : Block diagram for one area of sysem (i h area) compared wih a PI ype conroller whose parameers are uned using PSO oo. Simulaion resuls show ha he IP conroller guaranees robus performance under a wide range of operaing condiions and sysem uncerainies. PLAN OEL A four-area elecric power sysem is considered as a es sysem and shown in Fig.. he block diagram for each area of inerconneced areas is shown in Fig. (Wood and Wollenberg, ). he parameers in Fig. are defined as follow: ) : eviaion from nominal value i = H : Consan of ineria of i h area i : amping consan of i h area i : Gain of speed droop feedback loop of i h area i : urbine ime consan of i h area gi G i : Governor ime consan of i h area : Conroller of i h area Pdi u i : Load change of i h area : eference load of i h area B i = (/ i )+ i : Frequency bias facor of i h area P ie ij : Iner area ie power inerchange from i h area o j h area. where, i =,,,, j =,,, and i j he iner-area ie power inerchange is as () (Wood and Wollenberg, ): C ie ij = () i - ) j ) ( ij /S). () where, ij = 77 (/X ie ij) (for a 6 Hz sysem); X ie ij: Impedance of ransmission line beween i and j areas he )P ie ij block diagram is shown as Fig.. Figure shows he block diagram of i h area and Fig. shows he mehod of inerconnecion beween i h and j h areas. he sae space model of four-area inerconneced power sysem is as () (Wood and Wollenberg, ): where, &X = AX + BU Y = CX () U = [ )P )P )P )P u u u u ] Y = [ ) ) ) ) ) C ie, )C ie, )C ie, )C ie, )C ie, )C ie,] X = [ )P G )P )P G )P )P G )P )P G )P ) )C ie, )C ie, )C ie, )C ie, )C ie, )C ie,] he marixes A and B in () and he ypical values of sysem parameers for he nominal operaing condiion are given in appendix. As refereed before, he IP ype conroller is incorporaed o LFC problem. IP ype conroller is inroduced in he nex secion. 97

3 es. J. Appl. Sci. Eng. echnol., (): 96-, Fig. : Block diagram of iner area ie power ()P ie ij) U i U i,ref U O + Pl K P K I s Fig. : Srucure of he IP conroller IP Fig. 5: Oupu of IP and PI regulaors wih he same damping coefficien (> = ) and he same band widh a he same sep inpu signal command IP conroller: As referred before, in his sudy IP ype conrollers are considered for LFC problem. Fig. shows he srucure of IP conroller. I has some clear differences wih PI conroller. In he case of IP regulaor, a he sep inpu, he oupu of he regulaor varies slowly and is magniude is smaller han he magniude of PI regulaor a he same sep inpu (Sul, ). Also as shown in Fig.5, If he oupus of he boh regulaors are limied as he same value by physical consrains, hen compared o he bandwidh of PI regulaor he bandwidh of IP regulaor can be exended wihou he sauraion of he regulaor oupu (Sul, ). + ESIGN EHOOLOGY he proposed IP conroller performance is evaluaed on he proposed es sysem given in secion. he parameers of he IP conrollers are obained using PSO. In he nex subsecion a brief inroducion abou PSO is presened. Paricle swarm opimizaion: PSO was formulaed by Edward and Kennedy in 995. he hough process U o behind he algorihm was inspired by he social behavior of animals, such as bird flocking or fish schooling. PSO is similar o he coninuous GA in ha i begins wih a random populaion marix. Unlike he GA, PSO has no evoluion operaors such as crossover and muaion. he rows in he marix are called paricles (same as he GA chromosome). hey conain he variable values and are no binary encoded. Each paricle moves abou he cos surface wih a velociy. he paricles updae heir velociies and posiions based on he local and global bes soluions as shown in () and () (andy and Sue, ): where, V m,n P m,n new V m,n old local bes old = w V m,n + ' r (P m,n -P m,n ) + global bes old ' r (P m,n -P m,n ) () P new m,n = P old new m,n + ' V m,n () W r, r ' = ' local bes P m,n global bes P m,n = paricle velociy = paricle variables = ineria weigh = independen uniform random numbers = learning facors = bes local soluion = bes global soluion he PSO algorihm updaes he velociy vecor for each paricle hen adds ha velociy o he paricle posiion or values. Velociy updaes are influenced by boh he bes global soluion associaed wih he lowes cos ever found by a paricle and he bes local soluion associaed wih he lowes cos in he presen populaion. If he bes local soluion has a cos less han he cos of he curren global soluion, hen he bes local soluion replaces he bes global soluion. he paricle velociy is reminiscen of local minimizes ha use derivaive informaion, because velociy is he derivaive of posiion. he advanages of PSO are ha i is easy o implemen and here are few parameers o adjus. he PSO is able o ackle ough cos funcions wih many local minima (andy and Sue, ). IP conroller uning using PSO: In his secion he parameers of he proposed IP conrollers are uned using PSO. he IP conroller has wo parameers denoed by K P and K I and for each area here is one IP conroller. herefore in four-area elecric power sysem wih four IP conrollers, here are 8 parameers for uning. hese K parameers are obained based on he PSO. In secion, he sysem conrollers showed in Fig. as G i. Here hese conrollers are subsiued by IP conrollers and he opimum values of K P and K I are accuraely compued using PSO. In opimizaion mehods, he firs sep is o 98

4 es. J. Appl. Sci. Eng. echnol., (): 96-, Speed deviaions (p.u) Speed deviaions (p.u) Speed deviaions (p.u) ime (sec) (a) ime (sec) (b) ime (sec) (c) Fig. 6: ynamic response ) following sep change in demand of firs area ()C )a: Nominal b: Heavy c: Very heavy Solid (IP conroller), ashed (PI conroller) define a performance index for opimal search. In his sudy he performance index is considered as (5). In fac, he performance index is he Inegral of he ime muliplied Absolue value of he Error (IAE). IAE = ω d + ω d + ω d + ω d (5) he parameer "" in IAE is he simulaion ime. I is clear o undersand ha he conroller wih lower IAE is beer han he oher conrollers. o compue he opimum parameer values, a % sep change in P is assumed able : Opimum values of K P and K I for IP conrollers Firs area IP parameers Second area IP parameers.68. hird area IP parameers Fourh area IP parameers.55. able : Opimum values of K P and K I for PI conrollers Firs area PI parameers Second area PI parameers.978. hird area PI parameers Fourh area PI parameers able : 5% Sep increase in demand of s area ( C ) he calculaed IAE PI IP Nominal operaing condiion.59.9 Heavy operaing condiion.9.8 Very heavy operaing condiion.7.55 able : 5% Sep increase in demand of s area ( C ) and % sep increase in demand of rd area ( C ) he calculaed IAE PI IP Nominal operaing condiion.8.77 Heavy operaing condiion Very heavy operaing condiion.9.79 and he performance index is minimized using PSO. In order o acquire beer performance, number of paricle, paricle size, number of ieraion, ', ' and ' are chosen as, 8,,, and, respecively. Also, he ineria weigh, w, is linearly decreasing from.9 o.. I should be noed ha PSO algorihm is run several imes and hen opimal se of parameers is seleced. he opimum values of he parameers K P and K I are obained using PSO and summarized in he able. K P K P ESULS AN ISCUSSION In his secion he proposed IP conroller is applied o he sysem for LFC. In order o comparison and show effeciveness of he proposed mehod, anoher PI ype conroller opimized by PSO is designed for LFC. he opimumvalueofhe IP conrollers Parameers are obained using geneic algorihms and summarized in he able. In order o sudy and analysis sysem performance under sysem uncerainies (conroller robusness), hree operaing condiions are considered as follow: C Nominal operaing condiion C Heavy operaing condiion (% changing parameers from heir ypical values) C Very heavy operaing condiion (% changing parameers from heir ypical values) In order o demonsrae he robusness performance of he proposed mehod, he IAE is calculaed following sep change in he differen demands ()P ) a all K I K I 99

5 es. J. Appl. Sci. Eng. echnol., (): 96-, = A G G G G G G G G = B G G G G able 5: ypical values of sysem parameers for he nominal operaing condiion s area parameers =.5 G =.8 =.667 =. =.8 B =. =.5 =.5 =. =.55 =.5 =.6 nd area parameers =.5 G =.9 =.55 =. =.9 B =. =.5 =.5 =. =.55 =.5 =.6 rd area parameers =. G =.7 =.78 =.9 =.7 B =.8 =.5 =.5 =. =.55 =.5 =.6 h area parameers =. G =.85 =.5 =.995 =.9 B =.98 =.5 =.5 =. =.55 =.5 =.6 operaing condiions (Nominal, Heavy and Very heavy) and resuls are shown a able -. Following sep change, he IP conroller has beer performance han he PI conroller a all operaing condiions (able 5). Figure 6 shows ) a nominal, heavy and very heavy operaing condiions following % sep change in he demand of firs area ()P ). I is seen ha he IP conroller has beer performance han he oher mehod a all operaing condiions. CONCLUSION In his sudy a new PSO based IP conroller has been successfully carried ou for Load Frequency Conrol problem. he proposed mehod was applied o a ypical four-area elecric power sysem conaining sysem parameric uncerainies and various loads condiions. Simulaion resuls demonsraed ha he IP conrollers capable o guaranee he robus sabiliy and robus performance under a wide range of uncerainies and load Appendix: he ypical values of sysem parameers for he nominal operaing condiion are presened in able 5. Also he marixes A and B in () are as follow:

6 es. J. Appl. Sci. Eng. echnol., (): 96-, condiions. Also, he simulaion resuls showed ha he IP conroller is robus o change in he sysem parameers and i has beer performance han he PI ype conroller a all operaing condiions. EFEENCES Kocaarslan, I. and E. Cam, 5. Fuzzy logic conroller in inerconneced elecrical power Sysems for loadfrequency conrol. Elecr. Power Energy Sys., 7: Liu, F., Y.H. Song, J. a, S. ai and Q. Lu,. Opimal load frequency conrol in resrucured power sysems. IEE Proceedings Generaion, rans. is., 5(): andy, L.H. and E.H. Sue,. Pracical Geneic Algorihms, nd Edn., John Wiley & Sons, pp: erkpreedapong,., A. Hasanovic and A. Feliachi,. obus load frequency conrol using geneic algorihms and linear mmarix inequaliies. IEEE. Power Sys., 8(): Shayeghi, H., H.A. Shayanfar and O.P. alik, 7. obus decenralized neural neworks based LFC in a deregulaed power sysem. Elecric. Power Sys. es., 77: -5. Sul, S.K.,. Conrol of Elecric achine rive Sysems, John Wiley & Sons, Inc., Hoboken, NewJersey. an, W.,. UniWed uning of PI load frequency conroller for power sysems via IC. IEEE rans. Power Sys., 5(): -5. aher, S.A. and. Hemai, 8. obus decenralized load frequency conrol using muli variable QF mehod in deregulaed power sysems. Am. J. Appl. Sci., 5(7): Vrdoljak, K., N. Peric and I. Perovic,. Sliding mode based load-frequency conrol in power sysems. Elecric. Power Sys. es., 8: Wood, A.J. and B.F. Wollenberg,. Power Generaion, Operaion and Conrol. John Wiley & Sons. Zribi,.,. Al-ashed and. Alrifai, 5. Adapive decenralized load frequency conrol of muli-area power sysems. Elecrical Power Energ. Sys., 7: