Accelerating-Power Based Power System Stabilizers

Transcription

1 Acceleratng-Power Based Power System Stablzers G.R. Bérubé, L.. Hajagos, embers Kestrel Power Engneerng Ltd. ssssauga, Ontaro, Canada Abstract: Ths paper provdes an overvew of the key features of the acceleratng power-based power system stablzer (PSS). Ths desgn of PSS has been adopted by most major manufacturers and s ntegrated as an opton n many dgtal exctaton systems. The structure has been the topc of numerous publshed papers dscussng the choce of nput sgnals, parameter selecton and advantages over other conventonal PSS structures. Ths paper revews the key desgn prncples and applcaton ssues. Keywords: Exctaton Control, Power System Stablty, Stablzers, Ramp-Trackng Flters. I. INTRODUCTION Despte ther relatve smplcty, power system stablzers may be one of the most msunderstood and msused peces of generator control equpment. The ablty to control synchronous machne angular stablty through the exctaton system was dentfed wth the advent of hgh-speed excters and contnuously actng voltage regulators. By the md-96 s several authors had reported successful experence wth the addton of supplementary feedback to enhance dampng of rotor oscllatons []. The functon of a PSS s to add dampng to the unt s characterstc electromechancal oscllatons. Ths s acheved by modulatng the generator exctaton so as to develop components of electrcal torque n phase wth rotor speed devatons. The PSS thus contrbutes to the enhancement of small-sgnal stablty of power systems. any excellent references are avalable wth gudance on the selecton of PSS settngs once the requred speed sgnal s provded as an nput to the PSS [,3,4,5]. Early PSS nstallatons were based on a varety of methods to derve an nput sgnal that was proportonal to the small speed devatons characterstc of electromechancal oscllatons [,6,7]. After years of expermentaton the frst practcal ntegral-of-acceleratng-power based PSS unts were placed n servce [8,9,]. Ths desgn provded numerous advantages over earler speed-based unts and forms the bass for the PSS mplementaton that s used n most unts nstalled n North Amerca. Ths desgn s now a requrement n many Relablty Regons wthn North Amerca and has been modelled n the IEEE standards as the PSSA and PSSB structures []. For smplcty, the term PSSA stablzer wll be used to refer to the ntegral-of-acceleratng power based desgn n general throughout ths paper. Ths paper brefly descrbes some of the earler structures n order to explan the advantages of the acceleratng-power desgn. Ths desgn s then descrbed along wth a detaled revew of the role of the ramp-trackng mechancal flter and the bass for the present structure that s n wde use by many manufacturers. II. OVERVIEW OF PSS STRUCTURES Shaft speed, electrcal power and termnal frequency are among the commonly used nput sgnals to the PSS. Alternatve forms of PSS have been developed usng these sgnals. Ths secton descrbes the practcal consderatons that have nfluenced the development of each type of PSS as well as ts advantages and lmtatons. A. Speed-Based (Δω) Stablzer Stablzers employng a drect measurement of shaft speed have been used successfully on hydraulc unts snce the md-96s. Reference [] descrbes the technques developed to derve a stablzng sgnal from measurement of shaft speed of a hydraulc unt. In early desgns on vertcal unts, the stablzer s nput sgnal was obtaned usng a transducer consstng of a toothed-wheel and magnetc speed probe supplyng a frequency-to-voltage converter. Among the mportant consderatons n the desgn of equpment for the measurement of speed devaton s the mnmzaton of nose caused by shaft run-out (lateral movement) and other causes [,6]. Conventonal flters could not remove such low-frequency nose wthout affectng the electromechancal components that were beng measured. Runout compensaton must be nherent to the method of measurng the speed sgnal. In some early applcatons, ths was acheved by summng the outputs from several pck-ups around the shaft, a technque that was expensve and lackng n long-term relablty. The orgnal applcaton of speed-based stablzers to horzontal shaft unts (e.g. mult-stage 8 RP and 36 RP turbogenerators) requred a careful consderaton of the mpact on torsonal oscllatons. The stablzer, whle dampng the rotor oscllatons, could reduce the dampng of the lower-frequency torsonal modes f adequate flterng measures were not taken. In addton to careful pckup placement at a locaton along the shaft where low-frequency shaft torsonals were at a mnmum, electronc flters were also requred n the early applcatons [7]. Whle stablzers based on drect measurement of shaft speed have been used on many thermal unts, ths type of stablzer has several lmtatons. The prmary dsadvantage s the need to

2 use a torsonal flter. In attenuatng the torsonal components of the stablzng sgnal, the flter also ntroduces a phase lag at lower frequences. Ths has a destablzng effect on the "excter mode", thus mposng a maxmum lmt on the allowable stablzer gan [3]. In many cases, ths s too restrctve and lmts the overall effectveness of the stablzer n dampng system oscllatons. In addton, the stablzer has to be custom-desgned for each type of generatng unt dependng on ts torsonal characterstcs. The ntegral-of-acceleratng power-based stablzer, referred to as the Delta-P-Omega (ΔPω) stablzer throughout ths secton, was developed to overcome these lmtatons. B. Frequency-Based (Δf) Stablzer Hstorcally termnal frequency was used as the nput sgnal for PSS applcatons at many locatons n North Amerca. Normally, the termnal frequency sgnal was used drectly. In some cases, termnal voltage and current nputs were combned to generate a sgnal that approxmates the machne s rotor speed, often referred to as compensated frequency. One of the advantages of the frequency sgnal s that t s more senstve to modes of oscllaton between large areas than to modes nvolvng only ndvdual unts, ncludng those between unts wthn a power plant. Thus t seems possble to obtan greater dampng contrbutons to these nterarea modes of oscllaton than would be obtanable wth the speed nput sgnal [4]. Frequency sgnals measured at the termnals of thermal unts contan torsonal components. Hence, t s necessary to flter torsonal modes when used wth steam turbne unts. In ths respect frequency-based stablzers have the same lmtatons as the speed-based unts. Phase shfts n the ac voltage, resultng from changes n power system confguraton, produce large frequency transents that are then transferred to the generator s feld voltage and output quanttes. In addton, the frequency sgnal often contans power system nose caused by large ndustral loads such as arc furnaces []. C. Power-Based (ΔP) Stablzer Due to the smplcty of measurng electrcal power and ts relatonshp to shaft speed, t was consdered to be a natural canddate as an nput sgnal to early stablzers. The equaton of moton for the rotor can be wrtten as follows: where Δω = ( ΔP P ) t m Δ e () H H ΔP m ΔP e Δω = nerta constant = change n mechancal power nput = change n electrc power output = speed devaton If mechancal power varatons are gnored, ths equaton mples that a sgnal proportonal to shaft acceleraton (.e. one that leads speed changes by 9 ) s avalable from a scaled measurement of electrcal power. Ths prncple was used as the bass for may early stablzer desgns. In combnaton wth both hgh-pass and low-pass flterng, the stablzng sgnal derved n ths manner could provde pure dampng torque at exactly one electromechancal frequency. Ths desgn suffers from two major dsadvantages. Frst, t cannot be set to provde a pure dampng contrbuton at more than one frequency and therefore for unts affected by both local and nter-area modes a compromse s requred. The second lmtaton s that an un-wanted stablzer output s produced whenever mechancal power changes occur. Ths severely lmts the gan and output lmts that can be used wth these unts. Even modest loadng and unloadng rates produce large termnal voltage and reactve power varatons unless stablzer gan s severely lmted. any power-based stablzers are stll n operaton although they are rapdly beng replaced by unts based on the ntegralof-acceleratng power desgn. D. Integral-of-Acceleratng Power (ΔPω) Stablzer The lmtatons nherent n the other stablzer desgns led to the development of stablzers that measure the acceleratng power of the generator [,8,9]. The earlest systems combned an electrcal power measurement wth a derved mechancal power measurement to produce the requred quantty. On hydroelectrc unts ths nvolved processng a gate poston measurement through a smulator that represented turbne and water column dynamcs [6]. For thermal unts a complex system that measured the contrbuton of the varous turbne sectons was necessary []. Due to the complexty of the desgn, and the need for customzaton at each locaton, a new method of ndrectly dervng the acceleratng power was developed. The operaton of ths desgn of stablzer s descrbed n references [9,8]. The IEEE standard PSSA model used to represent ths desgn s shown as Fgure [].

3 Speed A Hgh-Pass Flters s Tw s Tw + s Tw + s Tw + s T6 + + Ramp-Trackng Flter C D E N (+s T8) + (+s T9) - Stablzer Gan & Phase Lead Ks + s T + s T + s T3 + s T4 Lmts Vstmax G H I Output Vstmn Ks3 Hgh-Pass Flters Power B s Tw3 + s Tw3 s Tw4 + s Tw4 Ks + s T7 F Fg. Acceleratng Power PSS odel (PSSA) The prncple of ths stablzer s llustrated by re-wrtng equaton () n terms of the ntegral of power. Δω = ( Pm Pe) t H Δ Δ () The ntegral of mechancal power s related to shaft speed and electrcal power as follows: Δ Pm t = H Δω+ Δ Pe t (3) The ΔPω stablzer makes use of the above relatonshp to smulate a sgnal proportonal to the ntegral of mechancal power change by addng sgnals proportonal to shaft-speed change and ntegral of electrcal power change. On horzontalshaft unts, ths sgnal wll contan torsonal oscllatons unless a flter s used. Because mechancal power changes are relatvely slow, the derved ntegral of mechancal power sgnal can be condtoned wth a low-pass flter to attenuate torsonal frequences. The overall transfer functon for dervng the ntegral-ofacceleratng power sgnal from shaft speed and electrcal power measurements s gven by: ΔP a ΔP(s) P(s) t e Δ G(s) e + +Δω H Hs Hs (s) where G(s) s the transfer functon of the low-pass flter. The major advantage of a ΔPω stablzer s that there s no need for a torsonal flter n the man stablzng path nvolvng the ΔP e sgnal. Ths allevates the excter mode stablty problem, thereby permttng a hgher stablzer gan that results n better dampng of system oscllatons. A conventonal end-of-shaft speed measurement or compensated frequency sgnal can be used wth ths desgn. (4) III Practcal Applcaton Issues any excellent papers have been wrtten dealng wth the tunng of PSS [4,5]. These authors dealt wth the selecton of phase compensaton, gan and output lmt settngs and ther effect on the overall performance of the PSS. Ths wll not be repeated here. Instead, ths secton wll focus on the dervaton of the acceleratng-power sgnal and ts use n dervng an equvalent speed sgnal. Specfcally, ths secton wll descrbe the mpact of speed measurement ssues and mechancal power varatons on the operaton of unts equpped wth ths style of PSS and how ths has nfluenced the desgn of PSSA stablzers. Wth a large base of nstalled unts, and long hstory of usage, experence has been acqured wth many dfferent vntages of hardware. Early desgns suffered from falures due to mechancal components such as speed pckups. Replacement of the measured speed sgnal wth a derved frequency sgnal has greatly mproved relablty at many facltes. The early analog-electronc desgns also suffered from relablty problems due to falures of components used to mplement the adjustable settngs (e.g. swtches, potentometers). Dgtal desgns have elmnated these components and mproved relablty and ease of use. Further gans n relablty are acheved when the PSS s mplemented as addtonal software code n a complete dgtal exctaton system, snce ths elmnates any addtonal hardware. A. Sgnal xng Referrng to the block dagram of Fgure, the two nput sgnals to the ΔPω stablzer are speed (A) and actve power (B). Although the ΔPω desgn has many advantages over stablzers that employ only one of these nputs t s senstve to the relatonshp between these two nputs. For optmum performance t s crtcal that the two sgnal paths (A-C and B- F) are matched n terms of gan and flter tme constants. 3

4 The power path employs two hgh-pass flter stages and an ntegraton to derve the ntegral-of-electrcal power change sgnal, ΔP e : ΔP e st W P e H + stw sh (5) st W3 K S Pe + stw3 + st7 The second part of Equaton 5 s based on the notaton of Fgure and the followng settngs: T W3 = T 7 = T W T W4 = (.e. ths block s bypassed) K S = T W / (H) K S3 = In order for the speed sgnal path to match the power path t must employ two stages of hgh-pass flterng as well, and ts equvalent flter tme constant must be kept as small as possble: T W = T W = T W T 6 Wth these settngs the sgnal appearng at pont D s proportonal to changes n the ntegral-of-mechancal power, ΔP m. When re-combned wth the ΔP e sgnal at pont G, the ntegral-of-acceleratng power, ΔP a, s formed. Ths sgnal s then treated as equvalent speed and the phase lead blocks that follow are set to compensate n order to maxmze the contrbuton of the stablzer to dampng torque. B. echancal Power Varatons Although the orgnal requrement for the PSS unts was based on a need to provde dampng for the local plant modes of oscllaton, many new nstallatons and retrofts have been appled to mprove dampng of nter-area modes of oscllaton [5] as s common n western U.S. utltes. In order to be effectve at dampng these modes of oscllaton, the hgh-pass flters, parameters Tw to Tw4 n Fgure, must be set to admt frequences as low as. Hz wthout sgnfcant attenuaton or the addton of excessve phase lead. Early attempts at re-tunng PSS for these frequences dentfed some sde effects related to mechancal power varatons on the unts. Tests on the orgnal ΔPω desgn on thermal unts ncluded fast ntercept valve closures that produced a step change n power of approxmately 5%, followed by a ramp of.55%/s [7]. The maxmum generator termnal voltage change produced by a PSS confgured wth short washout tme constants was below %, for the normal n-servce gan. On the frst tests of ths desgn on hydraulc unts, mechancal power ramp-rates n excess of %/s were acheved under gate lmt control. The ntroducton of long hgh-pass flter tme constants produced excessve termnal voltage and reactve power devatons. In response to ths problem, researchers dentfed the root cause of the varatons and modfed the desgns accordngly. When mechancal power s changed rapdly, electrcal power follows quckly but there s a lmted change n the rotor speed. Although ths depends on the strength of the system nterconnecton, the speed changes wll always be relatvely small and are consdered to be neglgble n the followng analyss. Referrng to Fgure, when electrcal power (B) s ramped, the ntegral-of-electrcal power sgnal (F) wll change wth a rate and magntude determned by the selected washout tme constants and unt nerta. From ths pont forward, the sgnal follows two paths to the output. The lower path s a drect connecton to the dervaton of the equvalent speed sgnal at pont G. The sgnal produced at pont F also travels through the mechancal power low-pass flter (E) before appearng at the output. Ideally these sgnals would exactly cancel each other, snce the PSS was not ntended to produce an output for ths condton. Wth long washouts and hgh ramp rates, ths s not the case and a large error sgnal can propagate to the PSS output, thereby changng termnal voltage and reactve power on the unt. Ths problem forced the selecton of low PSS gans or output lmts, severely lmtng the effectveness of the PSS. The transfer functon between the power nput, P E, and the ntegral-of-acceleratng power sgnal, P A, (ponts B and G n Fgure ) may be wrtten as follows: P(s) st K P(s) st st ( G(s) ) A W3 S = E + W3 + 7 The orgnal desgn of mechancal power low-pass flter conssted of a smple mult-pole flter of the form: G(s) = (+ st ) 9 whch s acheved n the model by settng the followng values: T 8 = N = The flter order,, and tme constant, T 9, can be selected to provde adequate attenuaton of the lowest torsonal frequency for horzontal-shaft applcatons. (6) (7) 4

5 Researchers [3] dscovered that they could reduce the senstvty to mechancal power varatons by re-desgnng the mechancal power low-pass flter to utlze a transfer functon of the form: G(s) ξ + s ω s ξ + s+ ωo ωo o = Further analyss and tests on actual hardware mplementatons confrmed that the complex-pole mplementaton was not optmal and that the followng transfer functon could be used to reduce mechancal power effects on the PSS output. N (+ st8 ) G(s) = (9) (+ st9 ) The flter of equaton 9 s frequently dentfed as a ramptrackng flter based on ts propertes when the coeffcents, T 8, T 9, and N are selected correctly. The crtera used to analyze the merts of dfferent mechancal power flter desgns are the followng: o o o (8) Attenuate hgh-frequency components n the nput sgnal. Allow low-frequency mechancal power changes to pass through wth neglgble attenuaton. nmze the PSS output devaton that occurs when the mechancal power s changng rapdly. Based on torsonal frequences as low as 7 Hz, the frst two crtera dctated the selecton of flters wth four poles (=4) and tme constants (T 9 ) of.8 seconds. These flters were used on numerous large horzontal unts but dd not meet the thrd crtera, especally when appled to hydroelectrc unts wth ther rapd ramp rates. To understand the advantages of the ramp-trackng flter and the requred selecton of coeffcents t s nstructve to compute the acceleratng power sgnal that s generated when mechancal power changes rapdly. For ths purpose, the ntegral-of mechancal power changes are characterzed as combnatons of the followng tme-doman nputs: o step, A*u(t) o ramp, B*t o parabola, C*t where t s tme n unts of seconds and A, B and C are the magntudes of the assocated components n per unt. The steady-state P A sgnal for each of these nputs can be calculated usng the fnal value theorem by evaluatng the followng: lm p (t) = lm (s* Input *(G(s) )) () A s Appendx A provdes detals of the evaluaton of equaton () for a conventonal low-pass flter (eqn.7) and the ramp-trackng flter (eqn.9). The result for each type of nput s summarzed n Table. Table : Steady State Response to Power Varatons Input Steady-State Output Low-Pass Ramp-Trackng step nput ramp nput -B**T 9 parabolc nput nfnte -C*F(,T 9 ) The key result n ths table s that the ramp-trackng flter produces a zero steady-state output for a ramp nput and a bounded output for a parabolc nput. Ths s only true f the coeffcents are selected to satsfy T = *T () 8 9 The dervaton of the results provded n Table, ncludng the relatonshp of Eqn() s ncluded as Appendx A. The most commonly used ramp-trackng flter coeffcents are N= and =5 snce ths provdes four net poles wth the mnmum number of numerator and denomnator terms. To obtan 4 db of attenuaton at 7 Hz, the denomnator tme constants are set to. s, resultng a numerator tme constant of.5 s. Wth ths desgn, the fltered ntegral-of-mechancal power sgnal can track rapd rates-of-change n the measured electrcal power sgnal, greatly reducng the termnal voltage modulaton produced by the PSS. Fgure dsplays the smulated output of stablzers equpped wth a conventonal and ramp-trackng low-pass flter to a power ramp on a hydraulc turbne. Clearly the ramp-trackng flter greatly reduces the PSS output devaton for ths condton. Dfferent coeffcents and tme constants can be used to mprove the trackng of power ramps or to provde greater attenuaton of low-frequency torsonal components. Increasng the denomnator order or the denomnator tme constant s a vable alternatve to ntroducng notch flters at torsonal frequences snce t does not nterfere wth the selected phase compensaton of the resultng acceleratng power sgnal. Ths wll ncrease the senstvty of the stablzer to power changes however ths s normally acceptable on large horzontal shaft unts wth ther slow loadng rates. 5

6 Actve Power PSS Output Fgure Smulated Ramp Response ramp-trackng low-pass Tme (seconds The performance of ths flter may also be crtcal to the behavour of the unt, n the event of nadvertent slanded operaton resultng n large frequency and mechancal power varatons. C. Input Sgnals Electrcal power s readly avalable as an nput. In analog mplementatons t can be measured usng a three-phase Halleffect watt transducer or equvalent devce that produces an nstantaneous output proportonal to the generator actve power. Selectve flterng s requred to remove the characterstc harmoncs present n the output measurement. In dgtal mplementatons a varety of technques are avalable to calculate power from the sampled ac voltage and current measurements. In ether case the key s to not add unnecessary flterng and phase lag that wll affect the phase compensaton n ths sgnal path. Ths has been acheved wth good success n varous manufacturers mplementatons for many years. The orgnal ΔPω stablzers employed a physcal measurement of shaft speed usng magnetc speed pckups as the source. A frequency-to-voltage converter was then used to generate the requred drect measurement of speed. Ths necesstated the use of flterng and as a result, the nput speed probe sgnals had to be relatvely hgh frequency, necesstatng multple probes and toothed wheel or mlled slot. Once agan careful selecton of the flterng was necessary to avod the ntroducton of phase lag n ths path. In applcatons where excessve flterng s used, the tme constant, T 6, can be used n the model of Fgure to smulate the effect on overall stablzer performance. Although there s a long hstory of speed measurement n exctaton control, t ntroduces several complcatons to the applcaton of the stablzer. Snce t requres the only movng parts n the entre devce, t s the least relable element of the desgn. Numerous stablzers have been temporarly dsabled or have faled durng operaton due to mproper gappng of speed measurement probes or falure of physcal or electrcal connectons. On vertcal shaft hydraulc unts, there was the sgnfcant addtonal complcaton of dealng wth shaft runout. On these unts there can be a sgnfcant lateral movement of the shaft that vares wth load level. Regardless of the locaton of the pckups, once-per-revoluton nose appears at some level. On unts wth speed n the range of rpm ths s very sgnfcant snce the nose component may concde wth the local mode electromechancal frequency of the unt. Early speed based stablzers coped wth ths problem through an ngenous mechancal arrangement that made use of up to 5 speed probes mounted equdstant around the crcumference of the shaft to elmnate the runout component [5]. Although ths worked and formed the bass for many successful stablzer nstallatons t was costly due to the need for customzaton at each locaton. It was also relatvely unrelable due to the requrement to have all probes n operaton for the cancellaton effect to functon properly. For these reasons, drect speed measurement was gradually phased out n favour of compensated frequency, whch can be measured usng the same PT and CT nputs that are already avalable for measurement of electrcal power. C. Compensated Frequency Drect termnal frequency, measured from the generator PTs, has been used as an nput sgnal n many stablzers n the past. Its advantages and dsadvantages were dscussed earler. It cannot be used drectly n a ΔPω stablzer confguraton. Referrng to the sgnal nomenclature of Fgure, t s a requrement that the speed sgnal at pont A match the power sgnal at pont B so that the derved ntegral-of-mechancal power sgnal at pont D represents equaton 3 accurately. Any error n the dervaton of the sgnal at pont D due to sgnal msmatch wll pass through the flter to pont E and wll result n an error n the stablzer output. The extent to whch the electromechancal components appear n termnal frequency s dependent on the component and the system strength. For example nter-machne modes between two unts connected together at ther low-voltage bus wll be completely absent n a frequency sgnal measured from the generator PTs. Inter-area modes nvolvng large groups of unts wll be vsble n the termnal frequency but local machne modes wll be greatly attenuated n for strong system connectons. Based on the above, frequency measurement can only be used f the ac source can smulate a voltage that s coupled drectly to 6

7 shaft poston changes. Both the generator termnal voltage and a voltage proportonal to the generator's termnal current are used n dervng the nternal voltage. A voltage behnd quadrature axs reactance s used for ths purpose: E = Et + jxqit () where Xq has been used to denote an mpedance proportonal to the generator s quadrature axs mpedance. Fgure 3 Compensated Phasor E Q-AXIS It Et jxqit The requrement for hgh relablty and mantanablty of PSS and other elements of the exctaton system may be n part satsfed by component redundancy. Duplcate voltage regulators and PSS [3,9] have been used on crtcal generatng unts. One voltage regulator wth ts PSS would be n servce at any one tme wth the other trackng t. In the event of a PSS malfuncton, varous protectve features would ntate transfer to the alternate regulator and PSS. In addton to mprovng the detecton of PSS falures, ths feature lmts the adverse consequences of such falures. The mproved relablty and reduced parts count of newer dgtal excters, wth bult-n PSS, have mtgated the need for such complex systems. Another feature worth ncorporatng n a PSS s bult-n faclty for dynamc tests. Ths allows routne testng of PSS perodcally by staton personnel n order to detect latent falures [9]. A convenent way to test the performance of a PSS s to nject a small ( to %) change n the PSS output (AVR termnal voltage reference) sgnal and montor the responses of key varables such as generator termnal voltage, feld voltage, power output, frequency, and PSS output. Such a test faclty s also very useful durng PSS commssonng. V. PSS COISSIONING AND FIELD VERIFICATION D-AXIS For steady-state condtons the phasor derved from the synchronous q-axs reactance wll be algned wth the quadrature axs s depcted n Fgure 3. As the rotor moves, the phasor derved n ths manner wll mantan ts poston where the frequency derved from the compensated phasor wll contan the desred electromechancal components. Snce the rotor s n moton, the compensatng reactance should represent the quadrature reactance that apples to the frequency range of nterest. For round-rotor machnes ths normally requres an mpedance value close to the transent quadrature reactance. Each generator wll be somewhat dfferent, and the compensatng reactance should be selected based on knowledge of the machne reactances and tme constants. IV. HARDWARE CONSIDERATIONS The hardware should be desgned so as to allow settng of the PSS parameters over a suffcently wde range. The desgn should also ensure a hgh degree of functonal relablty and allow suffcent flexblty for mantenance. These requrements are often overlooked, resultng n unrelable and unsatsfactory performance of the PSS, much to the frustraton of operators. There have been many nstances of operators turnng off the PSS because of poor performance resultng from nadequate hardware desgn and mproper selecton of control parameters. Durng feld commssonng, the actual response of the generatng unt wth the PSS s measured and used to verfy some of the analytcal results. Typcal tests performed durng commssonng nclude: measurement of the on-lne closed-loop exctaton system phase compensaton requrements (Fg. 4), step response tests to measure dampng mprovement at local mode frequences (Fg. 5), load-rampng tests to ensure that the PSS does not produce undesrable modulaton of the unt s termnal voltage under normal or emergency operatng condtons (Fg. 6) As noted n the prevous secton, the tests usually consst of njectng small step changes to the voltage regulator termnal voltage reference and montorng a number of generator varables. If there are dscrepances between computed and measured responses, the models are approprately modfed; f necessary, revsed PSS settngs are determned and mplemented. Ths "closed loop" desgn and commssonng process s very effectve [4]. 7

8 Fgure 4 Closed-Loop Excter Phase Compensaton stablzer phase compensaton closed-loop excter phase lag Tests and smulatons performed on all types of utlty-scale generators, ncludng large and small hydro, large fossl-fred and nuclear unts and combuston turbnes, have consstently demonstrated that a conventonal PSS tuned and tested n ths manner, wll mprove stablty for any reasonable operatng scenaro. Phase (degrees) washout& lag-lead selecton lead-lag selecton Reactve Power PSS Output Fgure 6. Fast Load Ramp Frequency (Hz) Intally, the PSS gan should be ncreased slowly, wth transent testng at each settng. To nsure suffcent stablty margn, a good practce s to check the performance of the PSS wth the gan ncreased up to twce the normal n-servce settng. The objectve s to ensure that the PSS gan s set at a value well below the lmt at whch ether the excter mode s unstable or there s excessve amplfcaton of nput sgnal nose. Fgure 5. Stablzer On-Lne Step Response Actve Power delta speed Actve Power Feld (Vdc) flter mech power Tme (seconds) delta speed Termnal V PSS Output PSS ON PSS OFF Tme (seconds) 8

9 Appendx A - Dervaton of Flter Responses A. Background The conventonal low-pass flter and ramp-trackng flter are both based on the general form of a flter: (+ st ) G(s) = (+ st ) 8 9 (A.) The steady-state response of the output, y, to varous nputs, u, s calculated from the fnal value theorem. lm y(t) = lm(s* U(s)*(G(s) )) (A.) s A. Conventonal Low Pass Flter The conventonal low-pass flter s obtaned from A. by settng T 8 =. The denomnator of A. can be expanded as follows: 9 9 ( st ) a (st ) + = (A.3) Some of the coeffcents may be wrtten by nspecton as follows: a = a = a = a - = The other coeffcents are not crtcal to the analyss of the steady-state response. Substtutng A.3 nto A. yelds: G(s) = a(st) st a (st ) = a (st ) (A.4) where the fact that a = has been used to reduce the numerator and expand the denomnator. Step nput: U(s) = A/s st a (st ) A lm y(t) = lm s s s a (st ) = Ramp nput: U(s)=B/s st a (st ) B lm y(t) = lm s s s a (st ) BT a a (st ) = lm s = B*T * Parabolc nput: C/s 3 lm y(t) = A.3 Ramp-Trackng Flter + st 8 G(s) = a(st) a (st 9) s(t T ) a (st ) = a(st) 9 (A.5) (A.6) (A.7) Step nput: U(s) = A/s (A.8) s(t8 T 9) a (st 9) A lm y(t) = lm s s s a(st) 9 = 9

10 Ramp nput: U(s) = B/s 8 9 (A.9) s(t8 T 9) a (st 9) B lm y(t) = lm s s s a(st) 9 = T T A.9 equates to zero as long as T 8 =*T 9 Ramp nput: U(s) = C/s 3 9 (A.) a(st) 9 C lm y(t) = lm s s 3 s a(st) 9 at as T = lm C s = CT a (st 9) The reducton s based on the assumpton that the coeffcent relatonshp, T 8 =*T 9, has been used. In ths case the response to a parabolc nput wll be bounded and wll ncrease wth the number of poles and tme constant as expected. References [] P.L. Dandeno, A.N. Karas, K.R. cclymont, and W. Watson, "Effect of Hgh-Speed Rectfer Exctaton Systems on Generator Stablty Lmts," IEEE Trans., Vol. PAS-87, pp. 9-, January 968. [5]. Klen, G.J. Rogers, S. oorty, and P. Kundur, "Analytcal Investgaton of Factors Influencng Power System Stablzers Performance," IEEE Trans. on Energy Converson, Vol. 7, pp , September 99. [6] W. Watson and G. anchur, "Experence wth Supplementary Dampng Sgnals for Generator Statc Exctaton Systems," IEEE Trans., Vol. PAS-9, pp. 99-3, January/February 973. [7] W. Watson and.e. Coultes, "Statc Excter Stablzng Sgnals on Large Generators echancal Problems," IEEE Trans., PAS-9, pp. 4-, January/ February 973. [8] F.P. deello, L.N. Hannett, and J.. Undrll, Practcal Approaches to Supplementary Stablzng from Acceleratng Power," IEEE Trans., Vol. PAS-97, pp. 55-5, September/October 978. [9] D.C. Lee, R.E., Beauleu, and J.R.R. Servce, "A Power System Stablzer Usng Speed and Electrcal Power Inputs Desgn and Feld Experence," IEEE Trans., Vol. PAS-, pp , September 98. [] J.P. Bayne, D.C. Lee, W. Watson, A Power System Stablzer for Thermal Unts Based on Dervaton of Acceleratng Power, IEEE Trans., Vol. PAS-96, Nov/Dec 977, pp [] IEEE Recommended Practce for Exctaton System odels for Power System Stablty Studes, IEEE Standard 4.5-5, Aprl 6. [] F.W. Keay, W.H. South, Desgn of a Power System Stablzer Sensng Frequency Devaton, IEEE Trans., Vol. PAS-9, ar/apr 97, pp [3] J..C. Soares, F.H. Pons, F.Rechert, D.O. Res, odellng and Feld Tests of a Supplementary Stablzng Sgnal for General Use, Natonal Semnar on the Generaton and Transmsson of Electrcal Energy, Brazl, 987. [4] P. Kundur, G.R. Berube, L.. Hajagos, R.E. Beauleu, Practcal Utlty Experence wth and Effectve Use of Power System Stablzers, IEEE PES eetng July 3, Vol 3, pp [] P. Kundur,. Klen, G.J. Rogers, and.s. Zywno, "Applcaton of Power System Stablzers for Enhancement of Overall System Stablty," IEEE Trans., Vol. PWRS-4, pp , ay 989. [3] P. Kundur, D.C. Lee, and H.. Zen El-Dn, "Power System Stablzers for Thermal Unts: Analytcal Technques and On-ste Valdaton," IEEE Trans., Vol. PAS-, pp. 8-95, January 98. [4] E.V. Larsen and D.A. Swann, "Applyng Power System Stablzers, Parts I, II, and III," IEEE Trans., Vol. PAS-, pp , June 98.