ANALYTICAL MODELLING OF HVDC-HVAC SYSTEMS

Transcription

1 ANALYTICAL MODELLING OF HVDC-HVAC SYSTEMS Dragan Jocc, Naln Pahalawaththa, Mohame Zaahr Member IEEE Member IEEE Unersty of Aucklan Unersty of Aucklan Trans Power NZ Lt Abstrt-A new HVDC-HVAC analytcal s presente n ths paper. The comprses of three subsystems: AC system, PLL an DC system. The s structure n such a manner to enable small sgnal analyss of HVDC-HVAC ntertons an possble problems arsng from these ntertons. CI- GRE HVDC Benchmark s use as a test system. erfcaton, performe usng PSCAD/EMTDC smulatons, showe goo response matchng for all DC an AC system arables. As an example of applcaton of ths the nfluence PLL ynamcs on the system stablty s stue offerng the mportant rules for tunng of PLL gans. Keywors: HVDC Transmsson, Power system lng, Phase locke loops, State spe methos. Nomenclature for AC-DC nterton arables: I I ψ, ψ E E ϕ, ϕ α β θ θ, rectfer, nerter AC current magntue, rectfer, nerter AC current phase angle,, rectfer, nerter AC oltage magntue, rectfer, nerter AC oltage phase angle,, rectfer, nerter frng angle orer,, rectfer, nerter PLL output angle,, rectfer, nerter tual frng angle,, e current, oltage nstantaneous alues. φ φ, E E rectfer, nerter oltage sturbance. I. INTRODUCTION Analytcal lng of HVDC systems has tratonally been regare as a ery ffcult task, an ts mportance has been ery often unerestmate n the presence of a large number of aalable smulaton pkages. Howeer, the approh base on the analytcal ng, for rehng generalse conclusons, or performng n-epth analyss, can not be matche by the tral an error type of stues carre out usng smulaton softwares. The analytcal, sought n ths paper, s ntene for analyss of prtcally obsere ssues assocate wth the operaton of HVDC systems. Of the specal mportance are: the secon harmonc nstablty (nclung the core saturaton nstablty an peroc nstabltes close to the frst harmonc) an, problems relate to the low SCR AC systems connecte to a DC system. Reference [], [] an a seres of relate references, offers the most rgorous an curate HVDC lng theory for the era of ts publshng. The mportance of curate screte conerter lng, was hghly emphasse n these references. Howeer ths has been at the expense of neglectng a number of ery mportant features n HVDC system operaton, partcularly relate to the HVDC-HVAC ntertons. Reference [3], presente the most comprehense HVDC reporte to-ate. It presente a systematc approh n bulng base on subsystem concepts, an usng the state spe representaton. The use of -q-0 transformaton for AC-DC couplng, although not preously unknown n HVDC lng [4], was also systematcally an effectely use n the system stablty analyss. There are howeer seeral aspects whch coul be further mproe n the aboe mentone HVDC : The s of the lnear screte type, whch s a great hancap when classcal control theory, so well eelope for lnear contnuous systems, nees to be employe. The oes not nclue ynamcs of Phase Locke Loop (PLL). The ynamc behaour, an the controller settngs of PLL on both ens of HVDC lnk, can hae sgnfcant mpt on the system stablty. A more conenent an a general metho for representaton of HVDC-HVAC ntertons woul enable effecte analyss of ntertons between the subsystems. It wll be shown n ths paper, that a lnear contnuous suffces for the nestgaton of most of the obsere operatng ffcultes, n general n the frequency range less than 00Hz on DC se. Rather than scretsng the, the lng approh n ths paper hghly stresses the m-

2 portance of AC-DC ntertons. Ths pont wll be further scusse n secton II. The sgnfcance of the HVDC ere n Reference [5], s the hgh leel of response matchng wth the PSCAD/EMTDC smulaton responses. Howeer snce the s eelope usng entfcaton methos, the usefulness of the n the system analyss an controller esgn s ery lmte. The states n the are entrely artfcal an they o not represent tual physcal arables. In contrast, the presente n ths paper, uses the states whch can be realy an prtcally obtane. Further, all AC-DC nterton equatons are purposely rearrange clearly showng the physcal relatonshp between the subsystem nterconnecton arables. In the stuy escrbe n reference [6], a lnear (contnuos) HVDC-HVAC s use for the analyss of secon harmonc nstablty at Chateauguay HVDC lnk. Howeer, the lng methos hae not been reeale. A. AC System II. SYSTEM MODEL The AC system eelope here nclues (Fgure ): The AC oltage source, whch s assume to be of constant magntue, phase an frequency ( es = const ). All phase angles are measure wth respect to the source oltage of one selecte phase. The equalent AC system harmonc mpeance charterstcs. The aopte secon orer AC equalent mpeance wll suffce for most stues. Incluson of hgher orer AC system representaton s a straghtforwar extenson of the. The nepenent phase system representaton of the three phase AC system also enables ng of the system phase asymmetry. AC system harmonc flters. Captors for rete power compensaton. The effect of electro-mechancal ynamcs of mhnes are not represente, for they are assume to be far below the frequency range of nterest n ths paper. If the stuy s neee n the lower frequency range, the can be expane to nclue the generator/loa ynamcs. As a stuy system, the CIGRE HVDC Benchmark [7], wth the AC systems whch nclue all the aboe system features (Fgure ), wll be use n ths paper. For the frequency range of nterest, any AC system can be reuce to an equalent shown n Fgure. For any phase of ths system, the states are chosen to be the nstantaneous alues of currents n the nuctors an oltages ross the captors. As an example for phase a, the selecte states are: [ ] x' = () a L L C L C C L C a T AC L R e s R L R 3 C L 3 R 4 C C 3 R 5 L 4 C 4 R 6 e Fgure. Structure of the test AC system. The complete three phase s expresse n the state spe form (or usng Laple operator s ): o x ' = A ' x ' + B ' u () sx' = A' x' + B' u ( ) y' C' x' = (3) where: x' x' = x' x' a b c, u = a b c, y e = e e an the matrces ( A', B' C') can be easly ere from the orgnal fferental equatons. In orer to represent the AC system together wth DC system n the same frequency frame, the effect of frequency conerson through AC-DC conerter s commoate usng Park s transformaton [8]. All three-phase AC system arables are conerte to -q arables through: x q = 0 Px ' (5) where P represents abc to q0 Park s transformaton. The eelope system has been lnearse aroun the nomnal operatng pont, an all states represente as aratons of -q components of corresponng arables. The arables pertnent to the zero sequence component n (5) hae been neglecte, snce t s known that the zero sequence components o not prouce any DC oltage. All nterton arables are expresse n terms of small eatons of ther magntue an phase angle. The AC system for rectfer or nerter AC system (=, respectely) s expresse n ts fnal form as: sx = A x + Bc uc + Bnp unp (6) y = C x c c (7) a b c (4)

3 where: u I = ψ, y E = c ϕ The ector u np n (6) represents the external sturbances for the AC system. Although the AC-AC ntertons are not consere n the test, t s clear that they can be realy nclue n (6). The aboe presente etale representaton of AC systems, enables the analyss of nfluence of arous AC system parameters nclung SCR aratons, on the system stablty. B. Phase Locke Loop Phase locke loops (PLL) use n HVDC conerters, hae tratonally eole oer seeral stages [9], an there s a we range of PLL types currently n use n HVDC schemes worlwe. The latest type of PLL (the D-Q-Z type) as presente n [9],[0] s consere n ths paper. Ths PLL type, shown n Fgure, s also use n []. The α an β components of AC oltages for D-Q-Z type PLL, are efne as: (8) Eα = Ea Eb E (9) c E β = E b c 3 ( E ) (0) Assumng that the lnearse equatons for ector transformer (9,0) are multple by the nherent PLL feebk loops (Fgure ) the error sgnal e can be ere. The error sgnal s a functon of AC oltage angle ϕ, an reference angle θ (PLL output). Ths error sgnal s use as the PLL controller nput. Conserng the ynamcs of VCO an PLL controller, the PLL s ere n state spe oman as: sx = k x + k u () PLL PLL PLL sxpll = kckpxpll + kcxpll + kckpupll () y = x (3) PLL PLL where: x PLL k ( ϕ θ) = s k, (4) c ( x PLL + kp ( ϕ θ ) s wth nputs an outputs to the PLL : u PLL = ϕ, y PLL = θ (5) C. DC system (conerter statons an DC lne) The DC system ere here comprses: DC lne represente as a T, as shown n Fgure 3. Rectfer an nerter current controllers (nerter s n beta constant moe). Smoothng retors; lumpe wth lne nuctance. Impeance of conerter transformers represente as an aerage retance oer one frng pero, n a manner smlar to that escrbe n []. Dynamc equatons whch escrbe AC-DC ntertons. In the eelope, n orer to ao the complex feebk loops between the subsystems an for the conenence of realy montorng an control, all the physcal nterton arables are efne as state arables. The ynamcs of these state arables are represente usng the well known statc equatons for AC-DC ntertons [8] together wth artfcally ntrouce ery small tme constant. Although ths approh coul ntrouce nstablty problems n the extreme cases, t has proe to be extremely useful n couplng between the subsystems. The lnearse ynamcs of DC system are represente n state spe oman as: sxc = Ac xc + Bc uc + Bcnp ucnp (6) y = C x c c c (7) where the ectors u c an y enote nterton arables whereas u cnp c stans for external nput sgnals, e.: E a E b E c 3ph/ph ector transformer 3ph/ ph E α E β X X + e Controller k p ω / s k / s c VCO reset at π θ V snθ V cosθ Fgure. D-Q-Z type phase locke loop.

4 u e c = E ϕ, u E ϕ cnp I = E E ref, y c I ψ = I ψ (8) Conerter operaton can be consere as a screte process operatng at a samplng frequency of tmes the nomnal AC frequency. Howeer most of HVDC-HVAC problems take ple n a frequency range aroun an below the AC system funamental frequency. For the analyss of such problems, the use of a contnuous nstea of screte seres as a suffcently curate approxmaton. Our smulaton tests hae shown that lnear contnuous s suffcent for stues of most of the HVDC operatng phenomenas, n the frequency range less then 00Hz on DC se. On the other han, f one requres to analyse the phenomena of HVDC systems closer to half the samplng frequency (6 tmes nomnal AC frequency), then a properly scretse system must be use []. When the propose s use for the controller synthess, a sgnfcant uncertanty n the hgher frequency range wll be nclue, to count for the neglecte screte system nature. D. HVDC-HVAC system The lnearse contnuous state spe of the oerall system can be obtane by combnng those s for the subsystems: AC system, PLL an rectfer-nerter-dc lne, ere aboe. The fnal s n the form: sx = Ax + B u (0) y a r np α np L r curr. contr. R r = Cx () where matrx A conssts of the system matrces of the three subsystems, an nterton matrces between the subsystems. Fgure 4 shows schematcally, how the subsystem s are connecte. The proceure outlne aboe escrbes the eraton for a two termnal HVDC system. Howeer, the structure C s I r I ref + R β=const Fgure 3. DC system representaton. L a e of the allows straght-forwar extenson to a DC multtermnal confguraton, where more than two AC systems are connecte to the DC system. Snce the s bult of subsystems, lnke together a a common state spe, the can be realy extene to nclue new subsystem s such as: atonal AC systems, AC oltage controllng elements an loa ynamcs. The small sgnal stablty analyss of the HVDC-HVAC system, can be one by performng the egenalue ecomposton analyss of eh subsystem, an of the oerall system. Important conclusons about the nfluence of eh subsystem on the oerall system stablty can be realy ere. Snce the uses physcally meanngful AC-DC nterton arables, the role of eh of these arables n the system stablty mproement/egraaton can be stue. For HVDC controller esgn, ths enables a systematc selecton of DC system arables an/or AC system arables as sutable feebk sgnals. III. MODEL VERIFICATION The PSCAD/EMTDC smulaton software s use for the erfcaton. The test system use s the CIGRE HVDC Benchmark [7],[], hang low SCR on both AC systems. The controller parameters (nclung PLL controllers) are taken from []. Fgure 5 compares the smulaton responses an the responses. For all of the system states, a goo matchng wth the smulator responses at lower frequences s obsere. Stll, as can be seen form the Fgure, some slght msmatch s apparent for the omnant oscllatory moe. The only reason for ths fference s the neglecte screte nature of the tual system. In. AC system Rec. AC system I ψ E In.PLL I ψ E Rec.PLL E ϕ θ φ β E ϕ θ φ α Conerter statons an DC lne DC cur. controller Fgure 4. Structural agram of the system. I I r I or

5 .090 Rectfer DC current ka eg eg eg Smulaton tme Rectfer AC oltage angle Smulaton tme Rectfer AC current angle tme Inerter AC current angle Smulaton Smulaton tme Fgure 5. System response followng current orer step change. Test system s the CIGRE HVDC Benchmark, Rec. SCR=.5, In. SCR=.5. Inerter operatng angle β = 40eg. Imagnary axs Imagnary axs Real axs Fgure 6. Influence of rectfer PLL gans. < < 00 Real axs Fgure 7. Influence of nerter PLL gans. < < 0

6 The use of non-scretse wll prouce ncorrect postonng of the system transmsson zeros, whch wll n turn cause ncorrect ampng of the omnant oscllatory moes. Howeer, these fferences are not sgnfcant. Our smulaton stues hae shown that the ere s relable for the system analyss an controller esgn at the frequences aroun (an aboe) the omnant oscllatory moe (70Hz) of the system. IV. INFLUENCE OF PLL GAINS Ths secton ges an example of the use n the HVDC-HVAC system analyss. Fgure 6 shows the moement of the system egenalues when the rectfer se PLL gan s. It can be seen that of PLL gan s ampng of omnant oscllatory moes. Fgure 7 shows that howeer the effect of PLL gan at nerter se s opposte to the aboe. For ery small gan the ampng of oscllatory moe at the lower frequency becomes sgnfcantly reuce. These conclusons also confrm that the ynamcs of PLLs use wth HVDC conerters, hae sgnfcant nfluence on the system stablty. V. CONCLUSIONS A new approh to the analytcal lng of HVDC- HVAC systems has been presente. The system conssts of three subsystems: AC system, PLL an DC system. The lnearse system ynamcs hae been represente n a common frame of reference wth respect to frequences by transformng the AC system arables to ts pseuo statonary -q-0 components. The stues hae shown that all HVDC- HVAC ntertons (nclung PLL ynamcs) nee to be represente n etal, whereas the scretsaton s not always necessary. Tme oman smulatons hae confrme that the ynamc performance of the ere closely matches that obtane from curate non-lnear smulatons. As t was expecte, some screpances n the responses are notce n the hgher frequency oman. The aantage of the ere s that t can be easly use for systematc analyss of, AC-DC an control ntertons as well as nfluence of arous system parameters on the system performance. As a emonstraton of the effecteness of the for analyss of HVDC-HVAC ntertons, the nfluence of rectfer an nerter PLL gans n ampng the omnant oscllatory moe has been stue. Ths stuy has shown that an n rectfer PLL gan wll the system ampng, whereas that of nerter eterorates the system stablty. REFERENCES: [] Sucena-Paa, J.P., Hernanez, R, Frers, L.L., Stablty stuy of controlle rectfers usng a new screte, Proc. IEE, Vol 9, no 9. Sep 97, pp [] Sucena-Paa, J.P, Frers, L.L., Stablty of rectfers wth oltage-controlle oscllator frng systems, Proc. IEE, Vol 0, no 6. June 973, pp [3] K.R.Payar, Shchanan Stablty of Conerter Control for Multtermnal HVDC Systems IEEE Trans on PAS, Vol, PAS 04, No 3, March 985, pp [4] H.A.Peterson, P.C.Krause, A Drect an Quarature-Axs Representaton of Parallel AC an DC Power Systems. IEEE Trans. on PAS ol. PAS-85, no.3 pp 0-5. [5] S.To, A.R.Woo, P.S.Boger, An S-Doman of an HVc Conerter IEEE-997, PE-96-PWRD [6] A.E.Hamma. "Analyss of secon harmonc nstablty for the Chateauguay hc/scc scheme". IEEE Transtons on Power Delery, 7() January 99, pp [7] M. Szechman, T. Wess an C.V. Tho. "Frst Benchmark for HVDC control stues", CIGRE WG 4.0 Electra No. 35 Aprl 99 pages: [8] Kunur,P Power System Stablty an Control McGraw Hll, Inc 994. [9] V.K.Soo, V. Khatr, H.Jn Performance Assessment usng EMTP of Two Gate Frng Unts for HVDC Conerters Operatng Wth Weak AC Systems IPST 95- Internatonal conference on power system transents, Lsbon, 3-7 September 995, pp [0] A. Gole, V.K. Soo, L. Mootoosamy, Valaton an Analyss of a Gr Control System Usng D-Q-Z Transformaton for Statc compensator Systems Canaan Conference on Electrcal an Computer Engneerng Montreal, PQ, Canaa September , pp [] D. Jocc, N. Pahalawaththa, M. Zaahr Harmonc Reucton n HVDC systems by Mofe DC Current Controller IPEC 97, Sngapore, May 997 Conference Proceengs pp [] Mantoba HVDC Research Centre, PSCAD/EMTDC Users Manual 994, Tutoral Manual BIOGRAPHIES Dragan Jocc obtane B.Sc (Eng) egree from Unersty of Belgrae, Yugoslaa n 993. He s currently workng towars PhD egree at Unersty of Aucklan, New Zealan. Hs research nterests le n the areas of control systems, HVDC systems an FACTS. Naln Pahalawaththa obtane the egrees, B.Sc (Eng) from Unersty of Moratuwa, Sr Lanka n 98 an PhD from Unersty of Calgary, Canaa n 988. He worke as a post octoral fellow at Unersty of Canterbury, New Zealan urng the pero an then jone the Unersty of Aucklan, New Zealan where he s presently a senor lecturer. Hs research nterests are power system analyss an control. Mohame Zaahr obtane the egrees, B.Sc (Eng) from Unersty of Peraenya, Sr Lanka n 987 an PhD from Unersty of Canterbury, New Zealan n 99. He worke as a post octoral fellow at Unersty of Canterbury, New Zealan urng an then jone Trans Power New Zealan Lmte where he s currently employe as Network Support engneer. Hs research nterests

7 are power system transents, nsulaton coornaton an HVDC transmsson.