FU RULE BSED LOD FREQUENC CONTROL IN RLLEL C DC INTERCONNECTED OWER SSTEMS THROUGH HVDC LINK S.Rmesh.Krishnn Reserch Scholr, nn University one 6, Slem (TN), Indi. Den, K.S.R. College of Engineering, Tiruchengode (TN), Indi. BSTRCT: In this pper, fuzzy logic controller is proposed for n ppliction of HVDC link to stbilize the frequency oscilltion in prllel C DC interconnected power systems. When n interconnected C power system is subjected to lod disturbnce, system frequency my be considerbly disturbed nd becomes oscilltory. By utilizing the system interconnections s the control chnnels of HVDC link, the tie line power modultion of HVDC link through interconnections is pplicble for stbilizing the frequency oscilltion of C system. The conventionl Integrl controller does not yield dequte control performnce. To overcome this problem Fuzzy Logic Controller (FLC) is employed with set of control rules. The proposed control technique is studied for two re non rehet therml power systems. From simultion results, the performnce of the FLC is better during lod disturbnces. KEWORDS: C DC Interconnected System, High Voltge Direct Current (HVDC) Link, re Control Error, Lod Frequency Control, Fuzzy Logic Control,. INTRODUCTION ower engineers hve the responsibility to deliver economicl, dequte nd qulity power to consumers. In order to chieve this, the power system must be mintined t the desired operting level by implementing modern control strtegies. The control of power systems is becoming incresingly more complex due to lrge interconnections. In n interconnected network, disturbnce in one line, leds to effects on the neighbouring systems chnge in tieline power nd frequency, cusing serious problem of Lod Frequency Control (FLC). LFC is simple mechnism to mintin or restore the frequency nd tie line power flow mong the interconnected power systems within the specified limit [, ]. LFC is very importnt fctor in power system opertion nd control for supplying sufficient nd relible electric power with good qulity. There hs been continuing interest in designing lod frequency controller with better performnce during the pst 3 yers. Mny control strtegy for LFC hve been proposed since the 97s [3]. Recently, pplictions of power electronics devices in C power systems provide ttrctive benefits of economics nd innovtive technologies. In prticulr, HighVoltge Direct Current trnsmission link (HVDC link) offers mjor dvntges in meeting these requirements, including long distnce overhed bulk power trnsmission, trnsmission between unsynchronized C systems [46], nd mrine cble trnsmission. sophisticted dvntge of HVDC link is the enhnced dmping of C trnsmission using power modultion vi n HVDC link in prllel CDC interconnected power system [4]. When n C power 78
system is subjected to lod disturbnce, the system frequency my be considerbly perturbed from the operting frequency. This my cuse severe problems in system frequency oscilltions. The devition of frequency oscilltions, tht exceed the norml limit, directly interrupts the opertion of power system. Moreover, the frequency oscilltions my experience serious stbility problems usully in the form of low frequency oscilltions due to insufficient system dmping. To overcome this problem, this pper not only tkes the dvntge of power modultion control offered by HVDC link to enhnce the system dmping, but lso extends to stbilize frequency oscilltions in n C power system. By utilizing the interconnections between C power systems s control chnnels of power modultion of HVDC link, this cretes new ppliction of the HVDC link to stbilize frequency oscilltions. Due to unnecessry error in the pst, conventionl I controller does not provide dequte control performnce. The difficulty in obtining the optimum settling time of previously sid controller is mitigted by using FLC [79], which gives the opportunity to describe the control ction in qulittive term nd symbolic form. The proposed control cn lso be coordinted with conventionl integrl control for greter efficiency. ROBLEM FORMULTION OF ROOSED CONTROL typicl two re interconnected system through C DC links is shown in Fig.. t re there is DC trnsmission line nd n inverter, wheres in re, the HVDC link minly consists of rectifier. Originlly re supplied power C through C line only, to re. It is ssumed tht in re there re lrge lods chnging suddenly, like mgnetic levittion trnsporttion, huge steel mills, re furnces etc. These cuse in re, sudden demnd for electric power nd serious problem of frequency oscilltions. In re, in ddition, there re mny independent power producers, hving no frequency control bilities sufficiently. s the cpbilities of frequency control governors in re re not sufficient, they re not cpble of stbilizing the frequencies oscilltions. Wheres re hs sufficient frequency control cpbility to compenste for re. C line lone cnnot supply the required bulk power. To supply move power to re, n C tieline in prllel with n HVDC link is lso provided from re. Through HVDC link, re offers frequency stbility to re [4]. The proposed method hs lrge cpbility of frequency stbilistion to other interconnected res hving less cpbility. The proposed control cn serve s new uxiliry service for stbilising future unregulted power systems. DESIGN OF OWER MODULTION CONTROLLER B HVDC LINK Coordinted Control of HVDC Link nd Governors To simplify the control design of the power modultion controller, the concept of coordinted control of HVDC link nd governors will be explined. The HVDC link is superior to the governor which is conventionl frequency control system in terms of highspeed performnce. Bsed on this different speed performnce, coordinted control of HVDC link nd governors is s follows. When some sudden lod disturbnces occur in n re, n HVDC link quickly strts the control system to suppress the pek vlue of trnsient frequency devition. Subsequently, governors eliminte the stedy stte error of the frequency devition. nother dvntge in considering the different 79
speed performnce is tht the dynmics of governors in both res cn be neglected in the control design of HVDC link for simplicity. Control Design The Linerized Model of Interconnected ower System without Governors for Control Design of ower Modultion Controller of HVDC Link is delineted in Fig. where the dynmics of governors in both res re eliminted. The power modultion controller is modeled s proportionl controller of ctive power. It should be noted tht the power modultion output of HVDC link (Δ DC ), cting positively on n re, rects negtively on nother re in n interconnected system. Δ DC, therefore, flows into both res with different sign (, ), simultneously. Here, to simplify the control design, the stte eqution of the system in Fig where the time constnt TDC is ignored, cn be expressed s S F C F T K S K S T F C F K S K S DC () method, so tht the dynmic spect of the interre oscilltion mode between res nd is specified. This mode cn be explicitly expressed fter pplying the vrible trnsformtion. CX () Where, C is trnsformtion mtrix, is the trnsformed stte vector, nd X is the stte vector in (). Therefore, the trnsformed system cn be expressed s k f 3 k C LOD D CHNGE R /ST HVDC OWER MODULTION CONTROLLER DC 3 C DC Kps/ST ps πt /S (3) Eqution () is referred to s system S. The vribles nd prmeters of in Fig re defined s follows. Δf, Δf re frequency devitions of res nd respectively. ΔC is n C tie line power devition between res nd. ΔDC is power modultion by HVDC link. Δ is the totl tie line power devitions (ΔC ΔDC ). Let M, M be the inerti constnts of res nd. D, D be the dmping coefficients of res nd. be n re cpcity rtio between res nd. Here, the control scheme for power modultion of HVDC link (ΔDC) is designed by the eigenvlue ssignment K ps/st ps Fig.. Linerized Model of Interconnected ower System without Governors for Control Design of The trnsformed coefficient mtrix of eqution (3) consists of two digonl blocks with complex eigenvlue α ± jβ nd rel eigenvlue λ. The complex eigenvlue physiclly correspond to the interre oscilltion mode, while the rel eigenvlue represents the system inerti center mode. From the physicl view point, it should be noticed tht the HVDC link between two res is effective to stbilize the inter re mode 8
only, nd therefore the input term of (3) corresponding to Δy3 is zero. This mens tht the HVDC link cnnot control the inerti center mode. To solve this crux, it is expected tht the governors in both res re responsible for suppressing the frequency devition due to the inerti mode. Therefore, the power modultion controller of HVDC link is designed bsed on stbilizing the interre mode. In order to extrct the subsystem where the inter re oscilltion mode between res nd is preserved, from the system S, the technique of overlpping decompositions5 is pplied. First, the stte vribles of the originl system S re clssified into three groups, ie x = [Δf], x = [ΔC] nd x3 = [Δf]. ccording to the process of overlpping decompositions [4], the system S cn be expnded s ~ S Where 3 x T, x T 3 T 3 3 3 33 nd B B B B3 DC x T, x T (4) T. The element ij, b i (i, j =,, 3) correspond to ech element in the coefficient mtrix in (). The system S in (4) cn be decomposed into two interconnected overlpping subsystems, ~ S ~ 3 S DC 3 33 B3 B B B DC 3 3 3 (5) (6) The stte vrible x, ie the C tie line power devition (ΔDC) between both res, is repetedly included in both subsystems, which implies Overlpping Decompositions. For system stbiliztion, consider two interconnected subsystems S nd S. The terms in the right hnd sides of (5) nd (6) cn be seprted into the decoupled subsystems (s indicted in the prenthesis in (5) nd (6)) nd the interconnected subsystems. s mentioned in Iked et l5, if ech decoupled subsystem cn be stbilized by its own input, the symptotic stbility of the interconnected overlpping subsystems S nd S re mintined. Moreover, the symptotic stbility of the originl system S is lso gurnteed. Consequently, the interctions with the interconnected subsystems in (5) nd (6) re regrded s perturbtions nd re neglected during control design. s result, the decoupled subsystems of S nd S cn be expressed s ~ S ~ S D D 3 3 33 In (7) nd (8), there is control input ΔDC ppering only in subsystem S D. Here, the decoupled subsystem S D is regrded s the designed system, which cn be expressed s F C TS T K T S S F C It cn be verified tht the eigenvlues of (9) re α ± jβ, ie, the interre oscilltion mode in the system S. It should be noticed tht by virtue of overlpping decompositions, the physicl chrcteristic of the originl system is still preserved fter the process. Here, the control purpose of HVDC link is to dmp the pek vlue of frequency devition fter sudden lod disturbnce. b b K T S S DC DC (9) (7) (8) 8
By eigenvlue ssignment method, the feedbck control scheme of ΔDC cn be expressed s DC k f k f C C () Note tht, the stte feedbck scheme is constructed by two mesurble signls, ie frequency devition of re nd n C tieline power devition. The integrl controller hs received gret del of ttention in the process control res. Integrl controller is device tht produces n output signl, which is integrl to the input signl. The system control outputs, which depends on the re control error, tht is given by () Bsed on the erlier reserch results of this stbilistion of frequency in the interconnected power system [], we cn design the fuzzy logic controller. Fuzzy set theory nd fuzzy logic estblish the rule of nonliner mpping. The use of fuzzy sets provides bsic for systemtic wys for the ppliction of uncertin nd indefinite models. two re interconnected power system with prllel C DC link is considered here s shown in fig.3. The overll system cn be modelled s multivrible system in the form of. X = x Bu Ed (4) () Where CE F ie CE ie ie F ie is the bising fctor nd U & U is the system control output. The integrl controller is successful pproch towrds the zero stedy stte error in the frequency of the system. The conventionl integrl controller, the gin K I hs been determined using Integrl Squre Error (ISE) criterion. The objective function used for this technique is (3) vribles s Where the System Stte vector x consists of nine u System control input is [u] = = u System disturbnce input vector is [d] = =, B nd E re system stte mtrix, distribution mtrix nd disturbnce distribution mtrix of pproprite dimensions. The min objective is to minimize the men squre error (MSE) of the re control error (CE) due to step type lod disturbnce [35]. The objective function of the lod frequency controller [4] is given by, d d c c d d Becuse of the complexity nd multivrible condition of the power system, conventionl model my not give stisfctory solution. This inference is further reinforced by fuzzy logic controller which is useful in mitigting wide rnge of control problem. Fuzzy Logic Controller: CE i = F i tiei (5) Where i vry from to is the bising fctor. 8
Membership vlue The design of LFC cn be normlly divided into three res nmely lloction of re inputs, determintion of rules nd defuzzifying of output into rel vlue. The method of fuzzifiction hs found incresing ppliction in power system. In this FLC, membership function (MF) specifies the degree to which given input belongs to set. In the cse of FLC, seven membership functions in tringulr shpe hve been chosen for the inputs of F i, tiei nd output (u). The linguistic descriptions of input membership functions re Negtive Lrge (NL), Negtive Medium (NM), Negtive Smll (NS), ero (E), ositive Smll (S), ositive Medium (M) nd ositive Lrge (L). The output membership functions re Negtive High (NH), Negtive Medium (NM), Negtive Smll (NS), ero (E), ositive Smll (S), ositive Medium (M) nd ositive High (H).the fuzzy membership functions for inputs nd output re shown in Figs. 4 nd 5. The union mximum opertion hs been selected for the fuzzy impliction. For the two input fuzzy system, it is generlly expressed s μ i( x) U i( x) = mx{ μ i( x), μ i( x) } (6) where i( x) nd i( x) re input fuzzy sets. The rule bse of the fuzzy controller reltes the premise ( Fnd tie ) to consequent (u). The structure of the control rules of the fuzzy controller with two inputs nd n one output is expressed s Membership vlue NL NM NS E S M L tie (b) Fig.5.Input membership functions of fuzzy controller () F; (b) tie NH NM NS E S M H Controlled output (u) Fig.6 Output membership functions of fuzzy controller Tble lists 49 linguistic fuzzy rules for the fuzzy controller. The centroid difuzzifiction hs been mde to find the crisp vlue of output. The centroid difuzzifiction is defined s n i= u i μ(u i ) U Crisp = (8) n i= μ(u i ) Where U Crisp is the output ofthe fuzzy controller, u i denotes the centre of the membership function of the consequent of the ith rule, μ denotes the membership vlue for the rule s premise nd n reperents the totl number of fuzzy rules. Tble, Fuzzy Control rules If (delf is NM or del tie is NS) then control signl u is NH (7) u tie NL NM NS E S M L Membership vlue NL NM NS E S M L F () F NL NH NH NH NH NS NM E NM NH NH NH NH NM E M NS NH NH NS NM E M S E NH NS NM E M S H S NS NM E M S H H M NM E M S L H H L E M S H H H H 83
β /R RE LOD CHNGER D(S) β CE C πt /S CE X e(s) g(s) /ST g /ST t Kps/ST ps k f k C /R /ST g /ST DC RE DC HVDC OWER MODULTION CONTROLLER X e(s) /ST t g(s) D(S) C πt /S K ps/st ps F (S) F (S) Fig. 3. Modeling of HVDC power modultor in the two re therml non rehet with prllel CDC power system Simultion Result nd Discussion: In this pper, two re non rehet interconnected system is used to design nd evlute the effects of the power modultion controller of HVDC link. The system dt re given in the ppendix. The simultion study is crried out by the softwre Mt lb. The system is simulted for step lod such s lrge steel roll mill nd rc furnce fctory, n increse % (.p.u.m.w.) occurs in re. Due to this, chnge in dynmic responses of the system hs been observed. Fig. 4 nd 5 indictes the frequency devition of re & nd fig. 6 indictes the tie line power devition for step lod disturbnce of re. Similrly the system is simulted for step lod disturbnce of 3% (.3 p.u.m.w.) occurs in re.for this disturbnce, the frequency devition of re & is shown in fig. 7&8. The tie line power devition for step lod disturbnce of re is shown in Fig.9. The effectiveness of the proposed control method is demonstrted by compring the integrl of the squre of the error (ISE), integrl of the bsolute vlue of the error (IE) nd settling time. 84
The ISE nd IE re given s ISE CE dt (9) IE CE dt () The performnce comprison for the step lod disturbnce of % nd 3% re presented in Tble Fig.4. Frequency devition in re(% Disturbnce) Tble, erformnce Comprison of different Control lgorithms Types of Control % Disturbnce ISE 3% Disturbnce % Disturbnce IE 3% Disturbnce Settling Time T s (S) % Disturbnce 3% Disturbnce Integrl Control.56.4.4.75 6. 8.6 Fuzzy Control.38..56.68 9.4.4 Fig.5. Frequency devition in re(% Disturbnce) It is observed tht the fuzzy logic controller exhibits reltively good performnces nd fst settling time. The conventionl integrl controller does not yield dequte control performnce.. Simultion result concludes tht fuzzy logic controller yields much improved control performnce thn the conventionl integrl controller. Fig.6. Tie line power devition (% Disturbnce) 85
logic controller is very effective in suppressing the frequency oscilltions cused by rpid lod disturbnces. For further study, the proposed control design of HVDC link will be extended to stbilize the frequency oscilltions in multi re interconnected power system. Fig.7. Frequency devition in re(3% cknowledgements: We would like to thnk rof. K. Nllthmbi nd rof. N. Kngrj, Deprtment of Electricl nd Electronics Engineering, K.S.R. College of Engineering, Tiruchengode, Tmilndu, Indi, for their vluble suggestions throughout this work. We lso thnk our mngement trustee K.S.R. College of Engineering for the fcilities provided to prepre this pper. References: [] George Gross nd Jeong Woo Lee, nlysis of Lod Frequency Control erformnce ssessment Criteri,IEEE Trnsction on ower Systems, vol 6,No. 3, ugust, pp5 55. [] Dulpichet Rerkpreedpong, mer Hsnovic nd li Felichi, Robust Lod Frequency Control using Genetic lgorithms nd Liner Mtrix Inequlities, IEEE Trnsction on ower Systems, vol 8,No., My 3, pp855 86. Fig.8. Frequency devition in re(3% Disturbnce) [3]F..deMellow, R.J.Mills nd W.F.B Rells, utomtic Genertion control, rt II Digitl control Techniques, IEEE Trnsction on ower pprtus nd Systems, vol. S9, No.3, My 97, pp76 74. [4] Issrchi Ngmroo, stbiliztion of frequency oscilltions in prllel C DC interconnected power systems vi n HVDC link, sciencesi8 (), pp 738. [5] Chidmbrm nd,velusmy.s., Decentrlized Bised Controllers for Lod Frequency Control of Interconnected ower Systems Considering Governor Ded bnd Non Linerity, IEEE Indicon, Dec 5, pp555. Fig.9. Tie line power devition (3% Disturbnce) Conclusion: In this pper, sophisticted method for stbilizing frequency oscilltions in prllel C DC interconnected power system through n HVDC link to stbilize frequency oscilltions in C power system cn be chieved. The HVDC power modultion controller is developed by pplying decomposition nd eigenvlue ssignment techniques. By simultion study, the fuzzy [6] Msil.M,Ghribi.M nd Kddouri., n dptive Fuzzy Controller Gin Scheduling for ower System Lod Frequency Control, IEEE (ICIT), 4, pp 555. [7] J. Tlq nd F. lbsri, dptive Fuzzy Gin Scheduling for Lod Frequency Control, IEEE Trnsction on ower Systems, vol 4, No., Februry 999, pp45 5. 86
[8] Vibhv Donde, M.. i nd In. Hiskens, Simultion nd Optimiztion in n GC System fter Deregultion IEEE Trnsction on ower Systems, vol 6,No. 3, ugust, pp48 487. [9] nnd.b nd Ebenezer Jeykumr.., Lod Frequency Control with Fuzzy Logic Controller Considering Non Linerities nd Boiler Dynmics CSE, vol8, issue 3, Jnury9, pp 5. [] Mthur.H.D. nd Mnjunth.H.V., Frequency Stbilistion using Fuzzy Logigbsed controller for multi re power system, South cific journl of Ntionl Science,vol.4, 7, pp 3. [] Chi Feng Jung nd ChunFeng Lu, ower System Lod Frequency Control By Genetic Fuzzy gin scheduling Controller, Journl of the Chinese institute of Engineers,vol.8,No.6,5, pp 3 8. ppendix: Two re Non rehet therml power system = =.45 p.u.m..w/hz. T t = T t =.3 sec T g = T g =.8 sec K ps = K ps = Hz/p.u. MW T =.545 T ps = T ps = sec R = R =.4 Hz/p.u MW. K f =.3 K C =.44 [] Chi Feng Jung nd ChunFeng Lu, ower System Lod Frequency Control By Evolutionry Fuzzy I Controller, IEEE, July4, pp7579. [3] Chowdhury. S, Chudhury. S. nd Choudhuri.S, dvnced digitl lod frequency control with unknown deterministic power demnd for interconnected power systems, IE (I) journl EL vol.8, Nov 999, pp 87 95. [4] Dulpichet Rerkpreedpong nd li Felichi, I Gin Scheduler for Lod Frequency Control Using Spline techniques,ieee,3, pp5963. [5] Ibrheem,.Kumr nd D..Kothri, recent hilosophies of utomtic Genertion Control Strtegies in ower Systems, IEEE Trnsction on ower Systems, vol,no., Februry 5, pp34 357. 87