Multiobjective Optimization of Load Frequency Control using PSO

Transcription

1 Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4) Multobjectve Optmzaton of Load Frequency Control usng PSO Santgopal Pan, Parmal Acharjee, Dept. of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, Inda Abstract Ths paper presents a practcal model for load frequency control (LFC) of two-area nterconnected power system. The proposed model s a non-lnear power system and s framed wth thermal generatng unts ncludng securty constrant governor dead band mposed by the governor. A Proportonal Integral Dervatve (PID) controller s used for the desgn and analyss of the proposed model. The Partcle swarm optmzaton (PSO) algorthm s developed to obtan sutable control parameters to acheve the optmum performance. A unque objectve functon s also formulated consderng the transent specfcatons. The closed loop performance s examned n the presence of constrant scenaro and the results and characterstcs show that the developed algorthm gves better performances. Keywords load frequency control; two area power system; governor dead band; PID controller; partcle swarm optmzaton I. INTRODUCTION For large scale nterconnected power system, load frequency control (LFC) s mportant to eep the system frequency and the nter-area te-lne power as close as possble to the schedule values. The frequency of a system s dependent on actve power balance. In an nterconnected system, wth two or more ndependently controlled areas, the generaton wthn each area has to be controlled so as to mantan scheduled power nterchange. The control of te-lne power and frequency s commonly nown as load frequency control (LFC). Recent growth and development of power system ndustry and ncreased power demand has necesstated ntellgent methodologes for practcal control of the power system. In modern days, smart grd predcts and ntellgently responds to actons of all supplers, consumers n order to effcently delver relable, economc electrcty servces. In smart grds, the use of renewable sources results n frequent varatons of frequency n the system as the power suppled s not constant. Regulaton of frequency can be done by control of load as well as the governor at the generatng statons. LFC usng controller based Dynamc Demand Control (DDC) can be used to mantan the frequency at nomnal value. Ths wll reduce the burden on generatng staton alone to regulate the frequency. In general, LFC s accomplshed by two dfferent control actons: prmary control and supplementary control. When load changes, the prmary speed control perform the ntal re-adjustment of the frequency and tepower by the acton of governor tself. The governor wll try to mnmze the frequency and te lne power devaton to zero by manpulatng nput to the turbne. The supplementary control acton s used to mnmze the frequency devaton, f persst after prmary control, to zero through ntegral control acton []. A systematc way of P, PI and PID controller parameters tunng based on Zegler-Nchols method for dstrbuted generaton system (DGS) was proposed n []. In recent past, advance control engneerng technques were used to desgn LFC system of large scale complex and uncertan power system. A robust control desgn that utlzes loopshapng deas for LFC regulaton was proposed n [3] consderng large uncertanty. Khodabahshan and Edrs [4] used a new tunng algorthm whch was based on maxmum pea resonance specfcaton supported by Nchols chart to tune the PID controller. In [5], a detal structured sngular value method and egen value method were proposed for local area and te-lne robustness analyss. A mult area adaptve LFC based on Self- Tunng Regulator (STR) for Automatc Generator Control Smulator (AGCS) was nvestgated n [6]. Alreza et al. [7] proposed a new robust optmal MISO- PID controller for LFC. In [8], two robust decentralzed control desgn methodologes were proposed. The frst one was based on H control desgn usng LMI technque and the second controller was a PI type, and was tuned by GALMI technque to mmc the same robust performance of the frst one. Yao Zhang et al. [9, ], developed an actve dsturbance rejecton control (ADRC) based robust decentralzed LFC soluton consderng wde range of parameter varatons, model uncertanty and large dsturbances. Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page 6

2 Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4) The controllers desgned so far usng tradtonal and advanced control technques for LFC system are model based controller. The performance of the controller s better on the specfc model. The performance of such controllers s not good enough for large power systems le power systems wth non-lneartes and not-defned parameters. Therefore, the desgn of ntellgent controller whch s robust and adaptve had been ntroduced to desgn the LFC system [-9]. In [], Taa-Sugeno fuzzy model of the power system was constructed for desgnng the fuzzy model based LFC. Bevran et al. addressed a new decentralzed fuzzy-logc based LFC scheme for mnmzaton of frequency devaton and telne power changes n the presence of hgh penetraton wnd turbnes []. An adaptve fuzzy gan schedulng scheme for conventonal PI and optmal controllers was proposed n [3]. Genetc algorthm (GA) based parameter optmzaton of PID sldng mode LFC used n automatc generatng control (AGC) of mult-area power systems wth non-lnear elements, was proposed n [4]. The decentralzed LFC was formulated as mult-objectve optmzaton problem n [5] and GA was used to tune the PI controller parameters of mult-area power system. The Partcle Swarm Optmzaton (PSO) algorthm, n ts dfferent form, have assumed much mportance n recent years for optmzaton of complex control problems and t s beng wdely used n LFC desgn. The LFC analyss for sngle and mult area power system usng PSO were reported n [6, 7]. PID gans of Sugeno fuzzy logc based automatc generaton control of mult-area thermal generatng plants were optmzed usng classcal partcle swarm optmzaton, hybrd partcle swarm optmzaton, hybrd genetc algorthm smulated annealng and was reported n [8]. In [9], load frequency stablzaton by coordnated control of thyrstor controlled phase shfters (TCPS) and super conductng magnetc energy storage (SMES) were nvestgated usng crazness-based partcle swarm optmzaton (CRPSO). From the above dscussons, t s obvous that PSO s a power full tool whch can be effectvely used to desgn the LFC system. For qualty electrc power servces, LFC s an mportant factor. The PID parameters of LFC system must be desgned n such a way that t ensures safe, relable and unnterrupted power supply. The classcal/conventonal approaches provde very poor performance for large networ under practcal constrants le governor dead band, generaton rate constrant, tme delay etc. The short comngs of the conventonal approaches are the motvatng factor of applyng soft computng technques for the desgnng of LFC system. Soft computng technques are not model specfc but t s robust n nature and can gve mult solutons. Under crtcal stuaton and securty constrants, soft computng technques can gve hghly satsfactory results. Ths paper presents a realstc approach to optmze the proportonal ntegral dervatve gans of load frequency control system. A two area thermal-thermal power system s consdered for the desgn purpose. For the two area case, the effect of governor dead band non-lnearty s taen nto account to mae ths approach a bt realstc one. The PSO algorthm s developed to optmze the PID gans and a novel objectve functon s desgned to calculate the optmal controller gans more accurately n least tme. The transent performance shows the sgnfcant superorty of the proposed desgn approach. II. SYSTEM MODEL A. LFC Model For understandng the control acton of LFC, consder the non-reheat thermal power system shown n Fg.. The basc bloc of power generatng unt conssts of the combnaton of governor, turbne and generator. As the load vares, the speed/frequency of the generator changes. The speed governor helps to match actve power generaton wth the demand by controllng the throttle valves whch montor the steam nput to the turbne. Governors are used to sense the frequency bas caused by load change and cancel t by varyng the nput of the turbne. The turbne unt s used to transform the natural energy, such as the energy from steam or water, nto mechancal power whch s suppled to the generator. The generator unt of the power systems converts the mechancal power receved from the turbne nto electrcal power. But for LFC, the focus s on the rotor speed output (frequency of the power systems) of the generator nstead of the energy transformaton. The lnear model of the LFC system s shown n fg. where the blocs are: non-reheat steam turbne = / ( Ts t ) ; load and machne = K / ( T s ) ; governor = / ( Ts ) ; p p Fg.. Model of sngle area power system g Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page 7

3 Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4) In the above confguraton, T g and T t are the governor and turbne tme constant. K p =/D and T p =H/fD where D s the rato of load changes percentage to the frequency changes percentage and H s the nerta coeffcent of generator. u s the load reference and P d s the load change. B. System Under Study As an example of mult area power system, we have consdered two area nterconnected power system for LFC analyss. In mult area power system, the prmary objectves of the LFC are to eep the system frequency at nomnal value, to provde load sharng between generators proportonately and to mantan the te lne power exchange at schedule value. For an nterconnected system, each area connected to others va te lne whch s the bass for power exchange between them. When there s change n power n area one, that wll be met by the ncrease n generaton n all the areas assocated wth a change n the te lne power and a reducton n frequency. But the normal operatng state of the power system s that the demand of each area wll be satsfed at a normal frequency and each area wll absorb ts own load changes. There wll be area control error (ACE) for each area and ths area wll try to reduce ts own ACE to zero. The ACE of each area s the lnear combnaton of the frequency and te lne error,.e. ACE = Frequency error + Te lne error. The transfer functon model of two area non-reheat thermal power system s depcted n fg. and the system parameters are gven n appendx A. To mae the analyss realstc one, the governor dead band s consdered n ths model whch mae the system nonlnear. A governor dead band s defned as the total magntude of a sustaned speed change where there s no change n valve poston of the turbne. The governor dead band non-lnearty tends to produce a contnuous snusodal oscllaton of natural perod of about T = s. The transfer functon of governor wth non-lnearty [7] can be expressed as: G( s) [.8 (. / )]/ ( st g ) () Fg.. Transfer functon model of two area nterconnected power system wth governor dead band III. PID CONTROLLER In ths study PID controller s used as a supplementary control for LFC. The PID controllers are wdely used n ndustry because of ts clear functonalty, easy mplementaton, applcablty, robust performance and smplcty. The transfer functon of PID controller s G ( s) Y( s) / E( s) K K / s K s () PID p d Where Y(s) and E(s) are the controller output and tracng error sgnals n s-doman respectvely. K p s the proportonal gan, K s the ntegral gan and K d s the dervatve gan. In PID controller, proportonal part reduces the error responses to dsturbances, the ntegral part mnmzes the steady-state error and the dervatve term mproves the transent response and stablty of the system. To get the optmum performance from the consdered system, the gans of the PID controller must be tuned n such a way that the close loop system produces desred result. The desred result should have mnmum settlng tme, no overshoot and zero steady state error. The parameters of the PID controller have been desgned usng developed PSO algorthm. IV. PARTICLE SWARM OPTIMIZATION Partcle swarm optmzaton s a populaton based stochastc optmzaton technque whch s ntroduced by Kennedy and Eberhart n 995 []. Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page 8

4 Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4) Ths computatonal technque s developed nspred by socal behavor of brd flocng or fsh schoolng. In ths technque, a group of random partcles (solutons) are generated. Accordng to ftness value the best soluton s determned n the current teraton and also the best ftness value s stored. The best soluton s nown as pbest. Another best ftness value s also traced n the teratons obtaned so far. Ths best ftness value s a global best and ts correspondng partcle (soluton) s called gbest. In every teraton all the partcles wll be updated by followng the best prevous poston (pbest) and best partcle among all the partcles ( gbest) n the swarm. The each partcle updates ts velocty and postons wth followng equatons: v w* v c* rand()*( pbest x ) c* rand()*( gbest x x x v (3&4) where =, n and n s the sze of the swarm, represent the no. of teraton. x : current poston of th partcle at th generaton v : current velocty of th partcle at th generaton pbest : pbest of th partcle for th generaton gbest : gbest of th partcle consderng the whole v w generaton.e. upto the th generaton : updated velocty of th partcle : nerta weght for th partcle c & c : constrcton factors rand () : random number between and. For the optmzaton process, f c & c are not selected properly accordng to the problem, the PSO system mght not converge at all. Usually c equals to c and ranges from [,4]. Inerta weght s another mportant factor for swarm optmzaton problems. Inerta weght (w) must not be constant for better results. It s randomly selected wthn a certan range. Random selecton of w provdes successful tracng for a dynamc optmzaton problem. The nerta weght w s determned accordng to the followng equaton: w ( w w )* present _ teraton max mum _ teraton max mn wmax (5) ) At the end of the teraton, the best poston of the swarm wll be the soluton of the problem. A smple PSO may not provde always the optmal soluton. The performance of the PSO can be mproved by modfyng the algorthm and proper selecton of constrcton factors and nerta weght. V. CONTROL STRATEGY The control confguraton for mult area power system s depcted n fg. 3. The error nput to the controllers are the respectve area control errors (ACE) gven by ACE B f Pte (6) where =,, B = frequency bas factor = (/ R) D Control nput to the power system s obtaned by use of PID controller together wth the area control errors ACE and ACE. The control nput of the power system u and u are the output of the controllers and these are obtaned as u K pace K ACE dt Kdd( ACE ) / dt (7) u K pace K ACEdt Kd d( ACE ) / dt (8) In LFC system, n order to convergence to the optmal soluton, two dfferent unque objectve functons are formulated. The objectve functons are derved consderng steady state and transent response specfcatons and proper selecton of weghtng factors. Wrong selecton of weghtng factors leads to ncompatble numercal value of each term of objectve functons whch gves erroneous result. To meet the desgn specfcatons, followng objectve functons are used. J ( e M ) ( SSE ) (9) 4 p J ( e M ) ( SSE ) () 4 p Where e and e = square ntegral of ACE and ACE, M p and M p = Maxmum overshoot of area- and and SSE and SSE = Steady state error of area- and. In ths paper, mult objectve optmzaton usng PSO algorthm s used to tune the PID control parameters. In mult objectve optmzaton, smultaneous optmzaton of multple objectves s carred out. Unle sngle objectve optmzaton, the soluton s not a sngle pont, but a group of solutons are obtaned whch may be useful for desgn and analyss. Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page 9

5 Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4) Fg. 3. Smuln model of the LFC system VI. RESULT AND DISCUSSION The smulaton s carred out by MATLAB 7.9 software run on a PC of dual core processor wth GHz speed and RAM of GB. For the mult area LFC system, the populaton sze s chosen as 4 and the maxmum no. of teratons for optmzaton are 4. Best value of constrcton factors c and c are taen as c=c=.5 and w max =.95 and w mn =.45. The smulaton s realzed n case of step load change, P L =. pu MW n area-, occurrng at t = sec and the frequency change n area-, area- and te-lne power change s observed. Ftness functon plot shown n fg 4, show the convergence characterstc of the proposed method. Ftness functon plot ndcates that the proposed algorthm requres around 3 teratons to converge. No sgnfcant change of the objectve functon values are observed after 3 teratons. The tuned parameters of the control system and the transent response specfcatons are shown n table. The results are compared wth Zegler Nchols tunng PID control method and PSO-PID method wth standard cost functon ISE [7].The observatons show that the proposed control strategy wth developed objectve functon produces good dynamc performances of the consdered power system. Specally, the proposed objectve functon extract better soluton compared to Zegler Nchols tunng method and PSO-PID method wth standard cost functon ISE where, Integral Square Error (ISE) = ( ACE ) dt () The transent response characterstcs of dfferent methods are depcted n Fgs Fg. 5 shows that Zegler-Nchols tunng method s able to mae steady state error zero. But t s ncapable of mang the maxmum overshoot and settlng tme mnmum. The number of oscllaton s also more n ths case whch mae the system relatvely unstable. It s observed from Fg. 6 that PSO-PID wth standard objectve functon produces good result compared to Zegler-Nchols tunng method. The maxmum overshoot and settlng tme becomes low and the no. of oscllatons s also reduced. It s clearly seen from the Fg. 7 and Table that the proposed PSO based PID controller wth the derved cost functon gves better control performance by mnmzng frequency and te lne power devaton to zero compared to other two technques. There s no oscllaton n the transent part whch mae the system relatvely more stable one.the proposed method yelds true optmal gans, mnmum settlng tme and zero overshoot of the transent responses compared to others and establshes ts superorty over the others. Table Controller parameters and transent specfcatons of two area power system by PSO-PID method Zegler- Nchols PSO-PID [wth standard cost functon ISE] Proposed PSO-PID Tepower Tepower Tepower K p K K d t s M p Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page

6 P te (p.u) P te (p.u) f f f f P te (p.u) ftness values/iteraton f f Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4).5 x -6 Ftness functon plot Vs. Iteraton J J No. of Iteraton Fg.4. Plot of objectve functons vs teraton of proposed method Tme (Sec) Fg.5. Frequency devaton of area- and and te lne power change wth Zegler Nchols method Tme (Sec) Fg.6. Frequency devaton of area- and and te lne power change wth objectve functon ISE usng PSO-PID method Tme (Sec) Fg. 7. Frequency devaton of area- and and te lne power change wth proposed method Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page

7 Internatonal Journal of Emergng Technology and Advanced Engneerng Webste: (ISSN 5-459, ISO 9:8 Certfed Journal, Volume 4, Specal Issue 7, Aprl 4) Internatonal Conference on Industral Engneerng Scence and Applcaton (IESA 4) VII. CONCLUSION In ths paper, PSO based PID controller desgn usng mult objectve optmzaton has been proposed for the LFC. It has formulated to optmze a composte set of objectve functons. A two area power system wth governor dead band has been consdered to demonstrate the proposed methodology. The objectve functons are unquely formulated by consderng the transent specfcatons and approprate selecton of weghtng factors. Smulaton results prove that the desgned PSO based PID controller gves very good transent and steady state performance for frequency and te lne power devaton compared to Zegler-Nchols tuned PID controller and PSO based PID controller wth standard objectve functon ISE. Due to ts smple structure and superorty, ths methodology can be appled to other control system problems. APPENDIX A The typcal values of the system parameters are gven bellow. T g = T g =.s; T t = T t =.3s; T p = T p = s; K p = K p = Hz/pu MW; T = T =.77 pu; R = R =.4 Hz/pu MW; B = B =.45 pu MW/ Hz. REFERENCES [] P. Kundur, Power system stablty and control, McGraw-Hll, New Yor, 994. [] G. Mallesham,S. Mshra, and A.N. Jha, "Maden applcaton of Zegler-Nchols method to AGC of dstrbuted generaton system", Power Systems Conference and Exposton, PSCE '9, IEEE/PES, pp.-7, March 9. [3] M tanov, G admor, and aharu, n robust control analyss and desgn for load frequency regulaton", IEEE Transactons on Power Systems, vol.3, no., pp , May 998. [4] Khodabahshan, and M Edrs, new robust PID load frequency controller, Control Engneerng Practce, vol. 6, ssue 9, pp. 69-8, September 8. [5] Wen an,and Hong Zhou, Robust analyss of decentralzed load frequency control for mult-area power systems, Internatonal Journal of Electrcal Power & Energy Systems, vol. 43, ssue, pp , December. [6] R.R. Shoults, and J.A. Jatva Ibarra, "Mult-area adaptve LFC developed for a comprehensve AGC smulator," IEEE Transactons on Power Systems, vol.8, no., pp , May 993. [7] Alreza Yazdzadeh, Mohammad Hossen Ramezan, and Ehsan Hamedrahmat, Decentralzed load frequency control usng a new robust optmal MI PID controller, Internatonal Journal of Electrcal Power & Energy Systems, vol.35, ssue, pp , February. [8] D. Rerpreedapong, A. Hasanovc, and A. Felach, A., "Robust load frequency control usng genetc algorthms and lnear matrx nequaltes", IEEE Transactons on Power Systems, vol.8, no., pp , May 3. [9] Yao Zhang, Ll Dong, and Zhqang Gao, "Load frequency control for multple-area power systems," Amercan Control Conference, ACC '9, pp , June 9. [] Ll Dong, Yao Zhang, and Zhqang Gao, robust decentralzed load frequency controller for nterconnected power systems, I Transactons, vol. 5, ssue 3, pp. 4-49, May. [] Ho Jae Lee, Jn Bae Par, and Young Hoon Joo, Robust load frequency control for uncertan nonlnear power systems: A fuzzy logc approach, Informaton cences, vol. 76, ssue 3, pp , December 6. [] H. Bevran, and P.R. Daneshmand, "Fuzzy logc based load frequency control concernng hgh penetraton of wnd turbnes", IEEE Systems Journal, vol.6, no., pp.73-8, March. [3] J. Talaq, and F. Al-Basr, "Adaptve fuzzy gan schedulng for load frequency control", IEEE Transactons on Power Systems, vol.4, no., pp.45-5, Feb 999. [4] L Pngang, Zhu Hengjun, and L Yuyun, "Genetc algorthm optmzaton for AGC of mult-area power systems," IEEE Regon Techncal Conference on Computers, Communcatons, Control and Power Engneerng, vol.3, pp.88-8, Oct.. [5] Fatemeh Daneshfar, Hassan Bevran, Multobjectve desgn of load frequency control usng genetc algorthms, Internatonal Journal of Electrcal Power & Energy Systems, vol. 4, ssue, pp , November. [6] S.K. Gautam, and N. Goyal, "Improved partcle swarm optmzaton based load frequency control n a sngle area power system", Annual IEEE Inda Conference (INDICON), pp.- 4, Dec.. [7] Asho Mohan Jadhav, and K Vadrajacharya, Performance verfcaton of PID controller n an nterconnected power system usng partcle swarm optmzaton, Energy Proceda, vol. 4, pp.75-8,. [8] P Ghoshal, Optmzatons of PID gans by partcle swarm optmzatons n fuzzy based automatc generaton control, Electrc Power Systems Research, vol. 7, ssue 3, pp. 3-, December 4. [9] Praghnesh Bhatt, P Ghoshal, Ranjt Roy, Load frequency stablzaton by coordnated control of thyrstor controlled phase shfters and superconductng magnetc energy storage for three types of nterconnected two-area power systems, Internatonal Journal of Electrcal Power & Energy Systems, vol. 3, ssue, pp. -4, December. [] Eberhart RC, Kennedy J, A new optmzer usng partcle swarm theory, In Proceedngs of sxth nternatonal symposum on mcro machne and human scence, Pscataway (NJ), IEEE Servce Centre, pp , 995. Department of Electrcal Engneerng, Natonal Insttute of Technology, Durgapur, West Bengal, INDIA. Page