Damping Algorithm based on Phasor Estimation

Transcription

1 Damping Algoritm based on Pasor Estimation Lennart Ängquist, Non-member IEEE ABB Power Systems AB S-7 64 Västerås, Sweden Abstract: Te paper describes a new metod to generate te reactance reference for a TCSC, wic as been installed in order to provide damping in a power system. Te knowledge of te expected oscillation frequency in te power system is used to create a coordinate system, wic rotates wit tat frequency. In tis coordinate system a pasor representing te power swing is being extracted from te input power signal. A reactance reference signal wit arbitrary gain and pase sift can easily be created using te pasor. Te pase of te reactance reference is preserved during limiting. ain and pase-sift may comfortably be sceduled due to measured parameters like erage power, power swing amplitude etc. Frequency compensation as been implemented, and adapts te frequency in te measuring system wen a power oscillation occurs. Te new approac as been implemented and successfully tested in te Nort-Sout Interconnection in Brazil in Marc 999 and as been in operation since ten. Te sceme is applicable for PSS and oter FACTS damping systems. Keywords: FACTS, TCSC, Controller Design, Power Oscillation Damping I. INTRODUCTION Te integration of two neigbouring power systems by an interconnecting line may often offer attractive benefits to bot parties. Te use of an AC intertie permits te investments to be spread in time to make pace wit te growing demand and opens te possibility to connect generation and/or load along te power line corridor. owever, in te initial stage of te power system integration, te power transfer capability of te interconnecting line may be low as compared to te installed power in te connected systems in te line terminals. Te integrated power system terefore is prone to low-frequency inter-area power swings, wen te equilibrium between generation/load balance in eac system and te power transfer along te interconnection line is being disturbed. Suc disturbances may e.g. be caused by trip of a generator or loss of a main transmission line. Te frequency of suc inter-area oscillations is low, typically in te range.-.4 z. Te very low frequency makes Power System Stabilisers (PSS less effective as te reactance between te inner emf in te generator and te terminal rater is te syncronous reactance tan te transient reactance. FACTS devices can be used to provide damping in tis situation. Tyristor Controlled Series Capacitor (TCSC as proven to be an effective means for tis purpose [-3]. Te TCSC is being Carlos ama, Member IEEE ONS R. da Quitanda Rio de Janeiro, RJ Brazil installed directly in te ig-voltage circuit witout any need for ig-voltage interfacing transformer. By tyristor control te inserted (capacitive reactance can be varied in order to dampen power oscillations. Wen a power oscillation occurs it is varied in pace wit te power swing and wit a pase sift of -9. A power disturbance in te interconnection line typically appears as in figure. p(t [MW] P (t+ p(t P (t Fig.. Typical power disturbance. t [sec] A sudden cange of te erage power occurs at te onset of te power oscillation. A ig-level power control system slowly restores te erage power towards a new equilibrium level by intervention to te power dispatc control. Te TCSC of course can not cange te erage power and it is supposed to react on te oscillation only. In order to control te TCSC so tat it brings about damping of te power oscillation it is crucial tat te oscillation part of te measured line power signal can immediately be extracted and separated from te cange in erage power. A furter requirement is tat correct pase sift sall be preserved even wen te reactance command is being limited to respect te maximum permitted main circuit stress in te TCSC. In tis paper a new approac, ere called te Pasor-POD, to solve tis problem will be reported. It is based on te fact tat te frequency of te potential inter-area power oscillation normally is quite well known. Te new metod takes advantage of tis information and continuously extracts a pasor tat represents te existing power swing wit te expected oscillation frequency from te measured power signal. In normal operation tis pasor is zero, but wen a power oscillation occurs te extracted pasor magnitude increseases in proportion to te swing amplitude. Its pase corresponds to te pase of te oscillation in te rotating

2 coordinate system. Te pasor representation is advantageous because a reactance command signal for te TCSC wit arbitrary gain and pase sift can easily be generated. Any implementation of FACTS apparatus reaces some maximum permitted stress wen te power swing amplitude and/or te gain is sufficiently ig. Its command signal ten must be limited accordingly. It is important tat te pase of te reactance control signal is not deteriorated by suc limiting actions. Altoug te power oscillation frequency is fairly well known some variations are caused by canging network configurations loading conditions etc. In order to exaust te maximum ailable damping performance of te installed TCSC te desired pase sift between te power oscillation and te reactance modulation signal sall be sustained in spite of small frequency variations. Te Pasor-POD concept compensates suc variations wen real power oscillations occur in te power system. II. CONVENTIONAL APPROAC Te traditional metod to generate command signal for damping devices like Power System Stabilisers (PSS and Static Var Compensators (SVC is to filter te power signal in a number of cascaded links. On or more wasout filters are used to remove te power erage. Te necessary pasesift is provided by lead-lag links. Te setup is depicted in figure. stw + st W + st + st + st3 + st 4 and simultaneously provide te correct pase sift wit respect to te power oscillation III. PASOR ESTIMATION Te Pasor-POD approac focusses on te problem of separating te power oscillation from te measured erage power. Tis is done by representing te measured line power in te form p ( { } j Ω t = P + e t Re ( were p(t is te measured line power, P is te erage P is a complex pasor tat represents te line power and power oscillation in a coordinate system, wic rotates wit frequency Ω.. Tus te idea is to extract te quantities,, wic are constants or at least slowly varying P functions of time. Because as soon as te constants in ( e been obtained it is an easy task to provide a damping signal D(t wit any gain and wit arbitrary pase. In te rotating coordinate system were P resides te damping signal is represented by te pasor k Pe were k is te gain and β is te desired pase sift. Te damping signal D(t can be obtained by transformation back from te original fixed coordinate system ( {( } j β k Pe e j Ω = t D t Re ( Te principle is illustrated in figure 3. Fig.. Conventional filter setup to create damping signal. p(t Coord transf & Pasor Estim P ke Coord transf to orig system D(t Additional links may be inserted to suppress interaction at lower or iger frequencies tan te intended ones. It sould be noted tat te design of te filters inerently utilises knowledge about te expected frequency of te power system oscillation and tey provide correct pase sift only at one specific frequency given by te design. Two major obstacles are encountered in tis approac: te cut-off frequency in te wasout filter must be well below te power oscillation frequency. Accordingly te (unwanted output signal caused by te erage power step does not disappear very fast at ig power swing amplitude it is necessary to limit te damping output signal so tat te main circuit of te damping equipment (TCSC, SVC or generator excitation system remains witin its dynamical range. It as proven to be difficult to accomplis adequate limitation Ω Ωt coordinate system angle integr Fig. 3. Principle for creating te damping signal. Te damping signal D(t represents te desired power modulation to be used for creating damping to te power system. In te case of a pure two-mass inter-area oscillation te pase sift will be selected to β=9, but for more complex swing patterns anoter pase sift may be preferred. It sould be noted tat te transfer function from intput p(t to D(t involves a coordinate transformation to and from te same rotating coordinate system. Tus, if te input signal varies sinusoidally wit frequency ω ten te output signal varies wit te same frequency ω.. In oter words te relation between te output signal D and te input signal p can be described by a linear transfer function.

3 Different tecniques may be used to extract te pasor. A straigt-forward engineering approac taking te expression ( as its starting point is derived in Appendix A. Its transfer function is given in Appendix B. An example of a transfer function as been depicted in figure 4. magn pase [deg].5.5 fs=.z, fcop=.6z, fcoav=.6z, k=, beta=9deg freq [z] Fig. 4. Transfer function (D/p in frequency domain. In te example te nominal frequency is. z and te pase sift is β=9. First order filters wit cutoff frequency.6 z are used. Te plots sow tat te Pasor Estimator as unity gain and te desired 9 pase sift at its nominal searc frequency. Te magnitude curve peaks at a somewat lower frequency. A more symmetrical caracteristics around te nominal frequency can be obtained by using second-order filters. Te gain at DC is zero. p(t ampl p-error [deg] fp=.z, nfilt=, fcop=.6z, fco=.6z Fig. 5. Time-domain response to suddenly applied sinusoidal signal Figure 5 sows te response in te pasor estimator wen a sinusoidal signal wit unity amplitude and nominal frequency is suddenly applied on its input. Te upper diagram sows te input signal in two cases wit different pase at te onset of te oscillation. Te diagram in te middle sows te estimated swing amplitude and te lower diagram sows te error of te estimated pasor. It can be seen tat almost correct amplitude and pase is obtained after approximately one cycle after te initiation of te oscillation. It was pointed out earlier (figure tat in a typical disturbance in te power transmission system a cange of te erage power appears at te onset of te oscillation. Te simulated response of te estimated pasor P for suc a disturbance is depicted in figure 6, were te input signal appears at te top and te diagrams below sow te estimated erage power, te swing amplitude and te error in pase error in te estimated pasor. Te tin curves indicate te ideal response. p(t [MW] pav [MW] psw [MW] p-error [deg] 5 fp=.z, nfilt=, fcop=.6z, fco=.6z Fig. 6. Pasor Estimator time domain response response to typical power oscillation disturbance. It can be concluded tat te erage power and pase information is obtained almost correctly witin less tan one cycle of te oscillation and tat te error in te swing amplitude is relatively small after a few cycles. For damping applications it is most important tat te correct pase is obtained. Errors in swing amplitude are less important. IV. REACTANCE MODULATION FOR DAMPIN In te Pasor-POD concept te problem of extracting te pasor representing te oscillation as been addressed separately witout considering oter requirements related to te damping device. Once te pasor as been extracted it is possible to comfortably make te necessary adjustments and adaptations of te damping signal so tat it fits wit te FACTS device tat will be used to bring about te damping action. In tis section adequate adaptations for a TCSC-based damping system will be discussed. Similar adjustments will be applied if te damper is any oter FACTS device or PSS. Te TCSC modulates te power flow on te transmission line by varying te inserted capacitive reactance. Te magnitude of te total compensating (capacitive reactance always is kept lower tan te inductive reactance of te line. Te power flow in te line is proportional to te inverse of te total reactance X LINE +X TCSC. Tus making te TCSC reactance more capacitive at any instant magnifies te amount of power flowing. In order to get a power modulation in accordance wit te damping signal te reactance command

4 must be multiplied wit te negative sign of te instantaneous power signal. ( p( t D( t X TCSC = sgn (3 Figure 7 illustrates equation (3 for tree different cases. p(t [MW] DXTCSC [oms] p(t > p(t crosses zero p(t < 5-5 Fig. 7. TCSC reactance order for different power oscillations. Te line current level, or equivalently te erage power level, determines te impact of te reactance modulation on te line power. At low current a muc larger reactance variation is required to obtain a certain power modulation tan at ig line current. Tis fact may be reflected in te selection of te gain for te damper. A multiplicative factor k according to figure 8 may be envisaged for tis purpose. P k P k Fig. 8. ain adaptation wit respect to erage power transfer level. Te network is small-signal stable under normal operating conditions in any realistic application. Te motivation for installing te FACTS damping device is to provide damping at major disturbances like loss of a generator or disconnection of a transmission line. owever, even in normal operation small oscillations do occur. Te damping equipment gets excited by tese small variations if te gain is ig. It is appropriate to operate wit low gain wen te swing amplitude is small and to increase te gain wen severe swings really occur. In tis way te termal capability of te TCSC is sed for intervention wen it is really required. Figure 9 depicts an example of suc a gain sceduling. Psw k Psw k Fig. 9. ain adaptation vs. swing amplitude. Te total gain is te product of te different gain factors k k k = (4 Sometimes it is adequate to adjust te pase sift from 9. Tis may e.g. be te case wen SVC is used to provide damping. It may even be desirable to adapt te pase sift in real-time wit respect to te actual power flow in te line. Tis may be easily be implemented in te Pasor-POD concept by a simple sceduling of β versus any relevant parameter. In te damping control signal in ( te limitations related to te maximum capability of te main circuit e not been considered. Its pase information terefore is unaffected by suc constraints. Te permitted operating range of a TCSC for power oscillation damping is depicted in figure. TCSC reactance [oms/p] CONT bypass mode MIN 3 TCSC operating range CONT 3 MIN SEC normal operation capacitive boost mode SEC Line current [A rms] Fig.. Typical operating range diagram for a TCSC designed for POD. Te reactance of te TCSC can be continuously varied on te capacitive side from te natural (negative reactance of te capacitor bank to a minimum reactance at maximum permitted tyristor boost. Tis limitation depends on te line current amplitude in order to limit te maximum capacitor voltage. It is advantageous to operate te TCSC wit low boost factor in steady-state conditions in order to minimise te losses and te armonic distortion of te inserted voltage. Terefore te dynamical reactance cange in te inductive direction, wic may be brougt about by boost factor adjustment, is small. Te TCSC owever offers te possibility of turning on te tyristors continuously to temporarily bypass te capacitor bank. Te TCSC, i.e. te capacitor bank and te inductor in parallel, ten inserts a low inductive reactance in te line. Tis bypass mode can be used wen big canges in te inductive direction are requested by te control. An adequate principle is to utilise te bypass mode wenever te reactance control signal exceeds te midpoint in te non-controllable reactance gap between te bypass and capacitive boost mode. Figure sows te result of tis principle in te case wen te oscillation amplitude decreases. It can be seen tat tis principle generates a reac-

5 tance variation wic retains te pase of te control signal. On te capacitive side te control signal will be limited at te maximum permissible boost level. xdamp [oms] xref [oms] inductive bypass switc level min boost - max boost -4 capacitive inductive - -4 capacitive time [sec] Fig.. Limitation of control signal for TCSC. V. FREQUENCY CORRECTION Te Pasor-POD extracts a pasor tat represents power swings wit te expected oscillation frequency all te time. In steady-state te extracted pasor is null. Te searc frequency as been determined from measurements or calculations. A pase error is obtained for power oscillations wit frequencies tat deviate from te searc frequency. It is natural tat small variations of te oscillation frequency occur due to varying network conditions, loads etc. owever, once a power oscillation arise te frequency error can be observed in te Pasor Estimator as a rotation of te estimated pasor. It is rater simple to arrange a frequency adjusting mecanism based on te requirement tat te pasor estimate sall e a constant argument in te rotating co-ordinate system. Simulations as sown tat it is advantageous to delay te release te frequency adjustment to about one cycle after te onset of a power oscillation. Figure depicts te frequency correction system in block form. abs startlevel t delay reaces te limit and remains tere for a considerable time te POD function will be disabled. Te reason for doing so is to prevent te TCSC from interacting wit oscillations tat emerge from oter sources tan te oscillations for wic te TCSC was intended. VI. NORT-SOUT INTERCONNECTION Te Nort-Sout Interconnection in Brazil was commissioned in te beginning of 999 [4]. Te km long transmission line is provided wit two TCSCs, one in eac end. A series of test were conducted in order to prove te effectiveness of te TCSC. A 375 MW ydro generator was tripped wen te network was intentionally weakened. Te results of two suc tests are sown in figure 3. Pline (MW No TCSC POD active 4 6 time (sec Pline (MW X TCSC time (sec Nort TCSC POD active time (sec Fig.. 3: Test record of POD using TCSC. Te upper diagram sows te power in te line and te lower diagram sows te reactance inserted by te TCSC. Two cases are recorded in figure 3. Te left-most curve sows te power oscillation wen no POD was active and te rigt-most curve wen te nort POD (using Pasor-POD control was active. Te registrations sow tat te system witout te POD is unstable, wile te single TCSC is able to successfully keep te system in syncronism during te disturbance. VII. CONCLUSIONS arg S& arg φ ref Σ (t PIcontroller Ω Σ Ω corr It as been sown in te paper tat te Pasor-POD concept is very useful for controlling FACTS damping devices like TCSC. Specifically it appears to be useful for adapting complex gain/pase sceduling. frequency controller VIII. REFERENCES Fig.. Frequency correction system Te frequency correction adjusts te Pasor Estimator frequency between certain rater narrow limits close to te expected oscillation frequency. If te frequency correction Ω [] L. Ängquist, B. Lundin, J. Samuelsson, Power oscillation damping using controlled reactive power compensation a comparison between series and sunt approaces, IEEE Trans. on Power Systems, vol.8, no., May 993, pp [] M. Noroozian, P. alvarsson,. Otman, Application of controlled series capacitors for damping of power swing, Proc. V Symposium of specialists in electric operational and expansion planning, vol., pp.-5, May 996, Recife, Brazil

6 [3] M. Noroozian,. Andersson, Damping of power system oscillations by controllable components, IEEE Trans. on Power delivery, vol.9, no.4, October 994, pp [4] C. ama, L. Ängquist,.Ingeström, M. Noroozian, Commissioning and operative experience of TCSC for damping power oscillation in te Brazilian Nort-Sout Interconnection, CIRE session, Paris, paper 4-4 APPENDIX A: DERIVATION OF A PASOR ESTIMA- TION ALORITM First rewrite equation ( as P = p = e jωt ( t Re( e jωt * jωt [ ( p( t P e ] (A Due to te assumptions made te rigt-and-sides of te equations in (A are constants or slowly varying functions of time. Terefore we obtain estimates P, P of te constants by applying low-pass filters to te rigt-and-sides of te equations. Ten te following algoritm is obtained P = = p p e ( t jωt, Re Pe jωt ( p( t P * e jωt (A were, LP p are operators representing low-pass filters. Typically first or second order filters wit a cut-off frequency at about.-.5 times Ω would be used. APPENDIX B: TRANSFER FUNCTION FROM MEAS- URED POWER TO DAMPIN SINAL p Assume tat te input signal is sinusoidal ( { j ω t ( } {( j ω Ω t Ae Ae t e j Ω = = Re t } Re (B were A is a complex constant. Te steady-state solution to (A ten as te form P jωt j( ω Ω t * j( ω +Ωt (B = B e = C e + C e were B, C and C are determined from te linear system and = = = p p B C = A C ( jω ( j( ω Ω ( j( ω + Ω (B3 (B4 Te transfer function from te input signal to te damping signal D output representing te erage power is obtained as jωt ( = Re{ ke e } = { k ( e j β C e j β C e j ω = Re + t } D t A comparison wit (B yields D D = k p ( e C + e C (B5 = (B6 XI. BIORAPIES Lennart Ängquist was born in Växjö, Sweden, in 946. e graduated (M.Sc. from Lund Institute of Tecnology in 968. e as been employed by ABB (formerly ASEA in various tecnical departments. e was working wit industrial and traction motor drives Tereafter e as been working wit FACTS applications in electrical power systems. Carlos ama was born in Minas erais, Brazil, in 959. e graduated in Electrical Engineering from Federal University of Rio de Janeiro in 98 and got is Master Degree (M.Sc. from Federal University of Santa Catarina. e as already worked for manufacturer, utilities as well as a consultant in power systems analysis, control and design. is as been working wit studies, design and implementation of DC links and FACTS devices in Brazil over te last 5 years. e is now working for ONS (Brazilian ISO and is a regular member of CIRÉ SC4.