Multi-Source Power System LFC Using the Fractional Order PID Controller Based on SSO Algorithm Including Redox Flow Batteries and SMES

Transcription

1 Int' Conf. Artfca Integence ICAI'6 Mut-Source Power System LFC Usng the Fractona Order PID Controer Based on SSO Agorthm Incudng Redox Fow Batteres and SMES H.A. Shayanfar * Department of Eec. Engneerng Coege of echnca & Engneerng, South ehran Branch, Isamc Azad Unversty H. Shayegh Department of Eectrca Engneerng, Unversty of Mohaghegh Ardab, Ardab, Iran A. Moaee Department of Eectrca Engneerng, Unversty of Mohaghegh Ardab, Ardab, Iran hashayanfar@gma.com, hshayegh@gma.com, amoaee.a@gma.com Abstract- Load Frequency Contro (LFC) of two-area nterconnected power system usng Fractona Order Proportona-Integra-Dervatve (FOPID) controer based on Soca Spder Optmzaton (SSO) agorthm s nvestgated n ths paper. he FOPID controer s a nonnteger order controer that mproves the performance of the nteger order PID controer. he dfference between the FOPID and PID controer s fractona order of ntegrator and dervatve n FOPID that make two degree of freedom n desgnng. In other word, the FOPID controer has fve parameters to be tuned for exact performance. Hence, SSO agorthm s chosen to optma tune the FOPID controer parameters n ths paper. he test system s the two area mutsource nterconnected power system ncudng reheat therma, hydro, gas and dese power pants. he proposed objectve functon conssts of Integra of me mutpy Absoute Error (IAE) pus sum of settng tmes of frequency devaton of each contro area and te-ne power fow devaton that are assocated wth proper weghted coeffcents. Aso, to show the stabty of FOPID controer the generaton rate constrant s consdered n ths study and the Redox Fow Batteres (RFBs) and Super Magnetc Energy Storage (SMES) s used to mprove the dynamcs of the system response under the oad dsturbances and system nonnearty. he smuaton resuts revea the good performance of the SSO based on FOPID controer n LFC probem. Keyword: FOPID controer, hree-area power system, SSO agorthm, GRC, SMES, RFB.. Introducton One of the most mportant ssues n power system operaton and protecton s keepng the frequency and votage n the nomna vaue or n predetermned mtaton. he reabty and quaty of generaton power depend on baance between the power generated and power demand pus power osses n a over the power system. When ths baance s dsrupted causes devaton n frequency and te-ne power. Aso, the oads are changed randomy. Hence usng a proper contro method t s necessary to prevent the power system to go to an unstabe state. So far, dfferent contro method have been used to contro the power system frequency n varous type of power system. Unt now, some revew artces n the LFC ssue have been pubshed []. In Ref. [] the Proportona-Integra (PI) based on fuzzy gan schedung consderng generaton Rate Constrant (GRC) has been proposed for a four-area nterconnected power system. he fuzzy PID type controer for oad frequency contro of two-area power system has been nvestgated n []. wo-degree-offreedom PID oad frequency controer n presence of GRC at the power generaton unt s performed n [4]. In [5] the robust PID controer s tunng based on maxmum peak of response specfcaton for Automatc Generaton Contro (AGC) n mut-machne power system. An adaptve PID has been tuned for LFC probem usng Neuro Fuzzy Inference System (ANFIS) and Artfca Neura Network (ANN) based on Genetc Agorthm (GA) [6]. Recenty, the researchers have used an mproved form of PID controer caed FOPID controer at the varous research works. In [7] the FOPID controer parameters has been optmzed usng CNC-ABC agorthm for Automatc Generaton Reguator. he FOPID controer s apped for stabty anayss and compensaton of reactve power n a mcro-grd [8]. he FOPID controer has two extra parameters more than PID controer that makes two degree of freedom n controer desgn and appcaton. Hence, the FOPID controer has been apped to oad frequency contro of two area mut-source nterconnected power system Correspondng Author, H.A. Shayanfar (hashayanfar@gma.com) ISBN: , CSREA Press

2 Int' Conf. Artfca Integence ICAI'6 consderng GRC and the Fexbe Aternatng Current ransmsson System (FACS) devces such as SMES, n ths paper. Aso, optma tunng of controer parameters to acheve the good performance and dynamcs response s necessary. he SSO agorthm s one of the heurstc agorthm that s beng used to sove the optmzaton probem. hs agorthm can baance exporaton and expotaton of soutons n the search space and prevent the premature convergence. Hence, the SSO agorthm s used for optmzng the FOPID controer to obtan the sutabe dynamcs response. he FOPID based on SSO agorthm has been apped on the two area mut-source nterconnected power system. he smuaton resuts show the good performance of ths approach to damp the frequency and te-ne devaton n the presence of oad dsturbances and nonneartes. Aso, the effect of SMES on mprovement of dsturbance reducton can be seen n the resuts.. Fractona cacuus here are dfferent defnton for Fractona cacuus and the Caputo's defnton [9] s chosen here and formuaton s as foows: Dt f () t ( n ) ( ) t (n)( ) f d () n t he above equaton s the fractona Dfferenta operator and the s the fractona order, m s an nteger, (.) s the Euer's gamma functon, n n and the other detas s descrbed n []. For usage of fractona operator n appcaton study, t s necessary that the approxmaton n nteger order transfer functon form be obtaned. In ths paper the Oustaoup s approxmaton [] s used for approxmaton and ts formuaton s as foows: P s s K () s P P.5( ) P h ( ) () P.5( ) h ( ) P (4) h P P K ( ) (5) Where, s the fractona order of dervatve, P s the number of zeros and poes, and s the th zero and poe n range of [, ], respectvey.. FOPID Controer h Defntey, the PID controer s one of the most appcabe controer that s used n ndustra appcatons []. In the [] an mproved form of PID controer s proposed by convertng the nteger order of dervatve and ntegrator nto the fractona order. hs controer s known as FOPID (PI D ) controer. Hence, the ony dfference between the PID and FOPID controer s the order of cacuus operators that make more degree of freedom and fexbty n desgn and practce. he mathematca formuaton of FOPID controer s as foows: C( s) S (6) S Where, the K P, K I and K D are proportona, ntegra and dfferenta gans and the and are fractona order of ntegrator and dervatve, respectvey. he structure of FOPID controer s gven n Fg.. K P K I K D 4. SSO Agorthm Fg.. FOPID controer structure he SSO agorthm s a swarm ntegence based agorthm that s proposed by Erk Cuevas et.a [] n. hs agorthm smuate the cooperatve behavor of the soca spders and ts mechansm s based on two dfferent search agent known as femae and mae spder. he SSO has a speca structure to fnd the soutons n the search space, so that t make the baance between exporaton and expotaton and aso, prevents fang nto the oca optmum. It s assumed that the a spders communcate wth each other by the communa web that makes the search space n ths agorthm. Actuay, the communa web s the nk that the spders transform nformaton through t and the nformaton s transferred usng the produced vbraton by the spders. he three dfferent types of vbraton nspred by boogca prncpes of the soca spders are modeed and descrbed foowng. Here, a bref of the agorthm s expaned and n deta expressed n []. he vbraton reazed by th spder as a resut of the nformaton transformed by jth spder and s as foows:, j j. d,j Vb w e (7) Where, the d,j s the Eucdan s norm between the spders and j. Smary, Vbc s the vbraton reazed by th spder as a resut of the transformed nformaton by the cth spder that has two major characterstcs as foowng: t s the nearest spder to th spder and has a hgher weght n comparson to (w c > w ). Vbf s the ISBN: , CSREA Press

3 Int' Conf. Artfca Integence ICAI'6 vbraton reazed by th spder as a resut of the transformed nformaton by the bth spder that has hghest weght n whoe popuaton. Vbf s the vbraton reazed by th spder as a resut of the transformed nformaton by the fth spder that s the nearest femae spder to the. he formuatons of above defnton about dfferent type of vbraton are gven foowng: d,c Vbc w. e (8) c d,b b. Vbb w e (9) d,f f. () Vbf w e he fowchart of the SSO agorthm s shown n Fg.. pant need to be controed by a controer, as a resut, there are sx FOPID controer and each controer has fve parameters that shoud be tuned usng SSO agorthm to acheve acceptabe response. Hgh performance of the proposed controer has been shown by apped on the tested system n the presence of nonnearty and uncertantes n the power system parameters. Furthermore, n order to mprove the dampng of the frequency devaton the RFB and SMES are consdered n smuaton. o evauate the performance of the SSO based FOPID controer t s need to dscuss some error crteron such as IEA and performance ndces such as settng tme and peak overshoot of power system response to oad dsturbances n dfferent operaton condtons. he proposed objectve functon s consdered as foows: Start Determne number of the mae and femae spders and ntaze them randomy Cacuate the weght for every spder Partcpatory operator move the femae spders (Cacuate Vbc and Vbb ) Dependng on the mae partcpatory operator move the mae spders (fnd the medan mae and cacuate the Vbf ) Accompsh the matng operaton and form the new popuaton usng rouette method Is Stoppng crtera s satsfed? Yes Prnt the best souton No Fg.. Fowchart of the SSO agorthm 5. FOPID Desgn for LFC Probem In ths paper, the FOPID controer based on SSO agorthm has been nvestgated for LFC n the two area mut-source nterconnected power system ncudng three generaton power n each contro area that can be seen at Fg.. he contro area- s consst of therma reheat, hydro and gas power pant and contro area- ncudng therma reheat, hydro and dese power pant [4, 5]. Each J a. IAE a.( OS ) a.(s) () tsm ( e ne ). o () IA E f f P tdt OS os os os () S st st st (4) Where, f and f are the frequency devaton n contro area- and area-, respectvey and Pe ne s te-ne power devaton. os, os and os are the peak overshoot and st, st and st are the settng tme of the frequency devaton of area-, area- and te-ne power devaton, respectvey. he a coeffcents are adjusted so that the a terms of Eq. () be n the same range. he GRC and SMES mode that have been used n ths paper are shown n Fg. 4 [5, 6]. he GRC s consdered % per mn at the therma unt n each contro area and the power system parameters are gven n Appendx. he SMES parameters must be optmzed to mprove the power system performance. he smuaton s performed for three case studes as foowng: Case. he FOPID controer has been apped on the two area mut-source nterconnected power system consderng GRC, ony. Case. he power system frequency has been controed n the presence of GRC and consderng the RFB n area- and SMES n area-. he FOPID controer parameters are optmzed usng SSO agorthm. he SSO and optmzed controer parameters are gven n abes and and the SMES parameters optmzed by SSO are shown n the abe. Aso, the frequency devaton of area- and area- and tene power devaton are seen n Fgs. 5 to 7. he IAE and performance ndces such as settng tme and peak overshoot of frequency and te-ne power devaton reated to both of cases are gven n the abe 4. ISBN: , CSREA Press

4 Int' Conf. Artfca Integence ICAI'6 Area B herma unt wth reheat turbne DP D RFB K Hydro unt wth governor _ ACE FOPID U K H ΔF Gas unt Area K G ΔPe herma unt wth reheat turbne K SMES Hydro unt wth governor ACE FOPID U K H ΔF Dese unt K D B DP D Fg.. Mut-source tow area nterconnected power system (a) (b) abe. Vaue of optmzed FOPID controer parameters usng SSO agorthm Contro Parameters herma Hydro Gas Dese Mode wthout RFB and SMES Area Area Fg.4. (a) he GRC mode for therma unt (b) he SMES mode abe. Vaue of SSO agorthm parameters for LFC probem Parameters Vaue Popuaton sze 5 Iteraton 5 Femae Percent 44 Mae percent 6 Upper mt of Kp, and + Lower mt of Kp, and - Upper mt of KSMES Lower mt of KSMES Upper mt of and Lower mt of and Upper mt of,,, 4 and SMES Lower mt of,,, 4 and SMES Mode wth RFB and SMES Area Area abe. Vaue of SMES parameters optmzed by SSO agorthm Parameter Vaue KSMES 4 SMES ISBN: , CSREA Press

5 4 Int' Conf. Artfca Integence ICAI'6 abe 4. Vaue of IAE and settng tme and peak overshoot wthout RFB and SMES Crteron Case Case Frequency Devaton of Area (Hz) IAE.8.94 Settng me (.%) Δf Δf ΔPe-ne Peak Overshoot Δf Δf ΔPe-ne - - x me (Second) Fg. 5. Frequency devatons of area for % step oad dsturbance n area ; Sod (wthout FRB and SMES) and Dashed (wth FRB and SMES) ffrequency Devaton of Area (Hz) x me (Second) Fg. 6. Frequency devatons of area for % step oad dsturbance n area ; Sod (wthout FRB and SMES) and Dashed (wth FRB and SMES) Power e-ne Devaton (p.u.).5 x me (Second) Fg. 7. e-ne power devatons for % step oad dsturbance n area ; Sod (wthout FRB and SMES) and Dashed (wth FRB and SMES) he settng tme of frequency devaton of area for case s.56 s and case s.94 s, same tme for frequency devaton of area s.96 s for case and s.776 s and for case, the settng tme of te-ne power devaton s.4 s for case and s.98 s for case. It can be seen the hgh effcency of the FOPID controer based on SSO agorthm n LFC probem and power system dynamcs response has mproved wth consderng RFB and SMES. Case. o ustrate the robustness of the SSO based FOPID controer, uncertantes n the power system parameters are consdered wth changng n range of [-%5, +%5] from the nomna vaue of some parameters ncudng t, w, cd and ps. he t, w, cd and ps s the tme constant of reheat turbne, tme constant of hydro turbne, gas turbne compressor dscharge voume-tme constant and power system tme constant, respectvey. he resuts of smuaton are shown n Fgs. 8 to. Frequency Devaton of Area (Hz) x me (Second) Fg. 8. Frequency devatons of area for % step oad dsturbance n area wth RFB and SMES, Dashed (-5% of nomna vaue), Sod (nomna vaue) and Dotted (+5% of nomna vaue Frequency Devaton of Area (Hz).5 x me (Second) Fg. 9. Frequency devatons of area for % step oad dsturbance n area wth RFB and SMES, Dashed (-5% of nomna vaue), Sod (nomna vaue) and Dotted (+5% of nomna vaue) e-ne Power Devaton (p.u.) x me (Second) Fg.. e-ne power devatons for % step oad dsturbance n area wth RFB and SMES, Dashed (-5% of nomna vaue), Sod (nomna vaue) and Dotted (+5% of nomna vaue ISBN: , CSREA Press

6 Int' Conf. Artfca Integence ICAI'6 5 abe 5. Vaue of IAE, settng tme and peak overshoot n presence of ±5% change n system parameters Parameters Change -5% Nomna Vaue +5% IAE Δf Settng me (.%) Overshoot Δf Settng me (.%) Overshoot ΔPe-ne Settng me (.%) Overshoot Based on the obtaned resuts of abe 5 and Fgs. 8- and comparson of IAE ndex, settng tme and overshoot for frequency devatons of each contro area, the good performance dampng of the proposed controer aganst varous uncertantes s acheved. hese outcomes show that the SSO based FOPID controer has a hgh abty n mprovement the dynamcs performance of the two area mut-source nterconnected power system n presence of dfferent operaton condtons and nonneartes such as GRC and uncertantes n the power system parameters. 6. CONCLUSION In ths paper, the FOPID controer based on SSO agorthm s proposed to sove the LFC probem n a mutsource two-area nterconnected power system. he objectve functon s combnaton of IAE and sum of settng tmes of the frequency devatons of each contro areas and te-ne power devatons. he resuts demonstrates that the SSO based FOPID controer assocated wth RFB and SMES have a hgh abty n dampng the frequency devaton of contro areas and tene power devaton. he contro parameters has been tuned usng SSO agorthm that s capabe at obtanng the optmum soutons n optmzaton probems. he proposed method has been apped on power system consderng nonnearty such as GRC and parameters uncertantes n power system. he resuts revea hgh abty of the proposed contro method to baance the power system frequency devatons n the presence of uncertantes, nonnearty n power system structure and oad dsturbance. APPENDIX he vaue of under study system parameters n Fg. are gven beow: f = 6 Hz; B = B =.4 pu MW/Hz; PR = MW (ratng), PL = 84MW (nomna oadng); r r = s; K r =K r =.; t t =. s;r = R = R = R 4=R 5=R 6=.4 Hz/pu MW; sg sg =.8 s;k =K =.54478;K H = K H =.684; K G =K G =.48; gh = gh =. s; rh rh = 8.75 s; rs rs = 5 s; W W = s; b g =.5; c g = ; X c =.6 s; Y = s; =. s; =.s; cd cd =.s;k Dese=6.5; c cr fc Dese =/ 4; ps ps =.49 s;k ps=k ps = Hz/pu MW; =.4 pu; REFERENCES [] Shayegh, H., H.A. Shayanfar, and A. Ja, Load frequency contro strateges: A state-of-the-art survey for the researcher. Energy Converson and Management, 5(): pp. 44-5, 9. [] Chang, C.S. and W. Fu, Area oad frequency contro usng fuzzy gan schedung of PI controers. Eectrc Power Systems Research, 4(): pp. 45-5, 997. [] Yeş, E., M. Güzekaya, and İ. Eksn, Sef tunng fuzzy PID type oad and frequency controer. Energy Converson and Management, 45(): pp. 77-9, 4. [4] an, W., unng of PID oad frequency controer for power systems. Energy Converson and Management, 5(6): pp , 9. [5] Khodabakhshan, A. and R. Hooshmand, A new PID controer desgn for automatc generaton contro of hydro power systems. Internatona Journa of Eectrca Power & Energy Systems, (5): pp. 75-8,. [6] Mosaad, M.I. and F. Saem, LFC based adaptve PID controer usng ANN and ANFIS technques. Journa of Eectrca Systems and Informaton echnoogy, (): pp. -, 4. [7] H. Shayegh, H.A. Shayanfar, and A. Ja, Mut stage fuzzy oad frequency contro usng PSO, Energy Converson and Management, 49: pp , 8. [8] Shayegh, H., A. Ja, and H.A. Shayanfar, A robust mxed H /H based LFC of a dereguated power system ncudng SMES. Energy Converson and Management, 49(): p , 8. [9] Yang, X.-J., Advanced oca fractona cacuus and ts appcatons. Word Scence, New York, NY, USA,. [] Oustaoup, A., X. Moreau, and M. Nouant, he CRONE suspenson. Contro Engneerng Practce, 4(8): pp. -8, 996. [] Åström, K.J. and. Häggund, Advanced PID contro. ISA-he Instrumentaton, Systems, and Automaton Socety; Research range Park, NC 779, 6. [] Podubny, I., Fractona-order systems and PI/sup/sp ambda//d/sup/sp mu//-controers. Automatc Contro, IEEE ransactons on, 44(): pp. 8-4, 999. [] Cuevas, E., et a., A swarm optmzaton agorthm nspred n the behavor of the soca-spder. Expert Systems wth Appcatons, 4(6): pp ,. [4] Parmar, K.P.S., S. Majh, and D.P. Kothar, LFC of an nterconnected power system wth mut-source power generaton n dereguated power envronment. Internatona Journa of Eectrca Power & Energy Systems, 57: pp , 4. [5] Sahu, R.K.,.S. Gorrpotu, and S. Panda, A hybrd DE PS agorthm for oad frequency contro under dereguated power system wth UPFC and RFB. An Shams Engneerng Journa, 6(): pp. 89-9, 5. [6] Bhatt, P., S.P. Ghosha, and R. Roy, Coordnated contro of CPS and SMES for frequency reguaton of nterconnected restructured power systems wth dynamc partcpaton from DFIG based wnd farm. Renewabe Energy, 4(): pp. 4-5,. BIOGRAPHIES Hedar A Shayanfar receved the B.S. and M.S.E. degrees n eectrca engneerng n 97 and 979, respectvey. He receved the Ph.D. degree n eectrca engneerng from Mchgan State Unversty, East Lansng, MI, USA, n 98. Currenty, he s a Fu Professor wth the Department of Eectrca Engneerng, Iran Unversty of Scence and echnoogy, ehran, Iran. Hs research nterests are n the appcaton of artfca ntegence to power system contro desgn, dynamc oad modeng, power system observabty studes, votage coapse, congeston management n a restructured power system, reabty mprovement n dstrbuton systems, ISBN: , CSREA Press

7 6 Int' Conf. Artfca Integence ICAI'6 smart grds and reactve prcng n dereguated power systems. He has pubshed more than 5 technca papers n the nternatona journas and conferences proceedngs. Dr. Shayanfar s a member of the Iranan Assocaton of Eectrca and Eectronc Engneers. Hossen Shayegh receved the B.S. and M.S.E. degrees n Eectrca and Contro Engneerng n 996 and 998, respectvey. He receved hs Ph.D. degree n Eectrca Engneerng from Iran Unversty of Scence and echnoogy, ehran, Iran n 6. Currenty, he s a fu Professor n echnca Engneerng Department of Unversty of Mohaghegh Ardab, Ardab, Iran. Hs research nterests are n the appcaton of robust contro, artfca ntegence and heurstc optmzaton methods to power system contro desgn, operaton and pannng and power system restructurng. He has authored and coauthored of 5 books n Eectrca Engneerng area a n Fars, one book and two book chapters n nternatona pubshers and more than papers n nternatona journas and conference proceedngs. Aso, he coaborates wth severa nternatona journas as revewer boards and works as edtora commttee of three nternatona journas. He has served on severa other commttees and panes n governmenta, ndustra, and technca conferences. He was seected as dstngushed researcher of the Unversty of Mohaghegh Ardab severa tmes. In 7 and he was aso eected as dstngushed researcher n engneerng fed n Ardab provnce of Iran. Furthermore, he has been ncuded n the homson Reuters st of the top one percent of most-cted technca Engneerng scentsts n 5 and 6, respectvey. Aso, he s a member of Iranan Assocaton of Eectrca and Eectronc Engneers (IAEEE) and senor member of IEEE.. Abdoah Moaee was born n Kermanshah, Iran, n 988. He receved the B.S. degree n Eectrca Engneerng from the Kermanshah Unversty of echnoogy, Kermanshah, Iran, n. He currenty s M.S. Degree student n Eectrca Engneerng from Unversty of Mohaghegh Ardab, Ardab, Iran. Hs areas of nterest n research are the Power System Restructurng and appcaton of heurstc optmzaton methods and robust contro desgn to power system contro ISBN: , CSREA Press