TRANSIENT PROCESSES AND DYNAMIC OF VARIABLE SPEED PUMP STORAGE UNIT

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1 Ol Shal, 203, Vol. 30, No. 2S, pp ISSN X do: 0.376/ol.203.2S Etonan Acadmy ublh TRANSIENT ROCESSES AND DYNAMIC OF VARIABLE SEED UM STORAGE UNIT RIMANTAS RANAS DEKSNYS *, DARIUS ALIŠAUSKAS Dptatmnt of Elctc ow Sytm Kauna Unvty of Tchnology Studntų t. 48, LT5367 Kauna, Lthuana Abtact. In th pap, a mathmatcal modl and th tuctu of vaabl pd pump toag unt (VSSU) a popod. Tannt poc of VSSU man paamt a analyzd. Th nflunc of tannt on th opatng condton of lctcal pow ytm dcud. Th ytm of nonlna dffntal quaton gvn n matx fom and pntng th VSSU mathmatcal modl olvd by dgtal ntgaton. Elctodynamc tannt of VSSU gnato and pump opaton a mulatd by mtaton of th actv and actv pow vaaton n th lctcal pow ytm. Magnal hydolctc paamt of th pump toag unt a valuatd. Exctaton contol algothm a bad on th functonal tuctu of voltag and cunt contoll pntd by compnaton unt contng of popotonal ntgatng and ntgatngdffntatng flt. Kywod: vaabl pd pump toag unt, dynamc modl, opatng chaacttc, fquncy contol, voltag qualty.. Intoducton Sval dcad ago vaabl pd pump toag unt w tatd to u fo dtmnng pmay and conday pow v of an lctcal pow ytm and fo balancng th changabl load pow. VSSU ffctvly u hydopow ouc and apdly pond to load pow chang []. Th applcaton of VSSU to th fat contol of actv and actv pow may cau hydaulc hock, ntablty of an lctcal pow ytm and axal vbaton of th VSSU oto. Ngatv conqunc may b avodd by th pop matchng of lctcal, mchancal and hydaulc paamt of VSSU, a wll a paamt of th xctaton contol ytm. Th qud qualty of fquncy and voltag n th lctcal pow ytm may b obtand by a labl contol of th ytm actv and actv pow * Copondng autho: mal manta.dkny@ktu.lt

2 Tannt oc and Dynamc of Vaabl Spd ump Stoag Unt 245 und VSSU gnato and pump opaton condton. It vy mpotant fo lctcal pow ytm ncludng wnd pow taton [2]. Thfo t ntal to valuat th pon of VSSU to th dbalanc of actv and actv pow n th lctcal pow ytm and fat contol dung gnato and pump opaton. Fo th pupo t ncay to dtmn functonal dpndnc of hydolctc paamt and chang paamt of th xctaton contol ytm accodngly. Th pap dal wth a mathmatcal modl of pow ccut and copondng computaton ndd fo analy of VSSU tannt. 2. Mathmatcal modl of vaabl pd pump toag unt Known mathmatcal modl of VSSU hav not bn contuctd uffcntly tctly and hould b modfd [2 5]. It ha bn tablhd that a unval mathmatcal modl of pow ccut dynamc dcbd by ytm of nonlna dffntal quaton havng ath complcatd oluton. Soluton utabl to comput th tm dpndnc of vaabl paamt may b dtmnd by th mthod of patal tat dgtal ntgaton. Th lctc ccut of VSSU cont of thpha ymmtcal tato and oto wndng. Th contucton mla to that of th aynchonou machn wth a phawound oto. Wth fnc to th fundamntal of th lctc ccut thoy quvalnt dagam of gvn atd pow VSSU lctc ccut copondng to dctax and quadatuax paamt a contuctd (Fg. ). a) d ax lctc quvalnt ccut d L ψ L ( ) ψ q d d d Lm d d b) q ax lctc quvalnt ccut ψ d L L ( ) ψ d d Lm q q Fg.. Equvalnt dagam of VSSU copondng to d and q paamt.

3 246 Rmanta ana Dkny, Dau Alšauka Equvalnt dagam (Fg. ) and th man paamt pntd by tato and oto actv tanc, nductanc L L, mutual nductanc L m, alo man quantt,.. tato and oto magntc flux n d and q dcton ψ and ψ, and tato and oto angula fqunc (dq) (dq) may b tanfomd to ak d and qcoodnat ytm copondng to on pha data. Nonlna ytm of dffntal quaton cont of Ohm and Kchoff law fo voltag of tato and oto ccut hown n th dagam of Fgu and copond to th chon dcton of cunt, voltag and magntc flux. Equaton fo th tato voltag pac phao balanc a th followng: = j ψ, j, d d d = ψ d () and quaton fo th oto voltag pac phao may b wttn mlaly: = j ( ) ψ, j ( ). d d d q q q = q ψ d Th ytm alo upplmntd wth th momnt of momntum quaton accodng to Nwton cond law: (2) d J = T ± Tm D, (3) wh T and T m a lctomagntc and mchancal dvng toqu and D th dampng coffcnt. Th matx fom of th quaton ytm ( 3) th followng: d d ψ d q ψ d ψ d d d = t t. d d d ( ) ( ) ψ ψ q q q ( ) ψ ( d ) ψ d ψ q (4)

4 Tannt oc and Dynamc of Vaabl Spd ump Stoag Unt 247 Fo mplfyng calculaton magntc flux phao componnt n matx quaton (4) may b placd by poduct of cunt and nductanc: dd dd L L Lm q Lm d d d q dl L dlm L m =. d dd dd L ( ) Lm L ( ) ql q d d q ( ) dlm L ( ) dl L Inductanc matx dtmnd fo ntal ntant whn angula fqunc of th tato and oto a qual to zo ( = 0, = 0 ): L 0 Lm 0 0 L 0 L m L =. (6) Lm 0 L 0 0 Lm 0 L Aft om manpulaton wth momnt of momntum quaton (3) and matx quaton (5), w gt a ytm of quaton fo pac tat vaabl n Cauchy fom: d d d d = A B d d d q q q d θ θ = A2 B2 (5), (7) wh A, and B a th tato and oto coffcnt matx; A 2, and B 2 a momnt of momntum coffcnt matx. By ubttutng matx quaton (5) fo momnt of momntum quaton (3) n ytm (7), th coffcnt matx pntng VSSU pac tat quaton wth pct to th tato and oto cunt phao and oto cunt fquncy may b obtand:

5 248 Rmanta ana Dkny, Dau Alšauka d L 0 L d m L Lm 0 = L d 0 ( ) Lm ( ) L q ( ) Lm 0 ( ) L d d L { E, d B d q q 0 0 d θ θ D, = 0 ( T ± Tm) 4243 J J A2 B2 wh E th unt matx, θ th angl of oto, Tm = Tm(g) th ngatv momnt of momntum fo gnato opaton, and T m = T m(p) th potv momnt of momntum fo pump opaton. Valu of tato and oto cunt at gvn ntant t and alo valu of oto angl and oto angula fquncy a dtmnd fom quaton (7) and (8) by dgtal ntgaton: A (8) d d d t () A t ( h) () t = () t ( ) (τ) dτ d A d B 0 d q q q, (9) t θ () t θ A2 A2( h) () t = () t (( ) ) dτ B2 0 wh h = t τ th ntgaton tp and τ th tm dlay. Summay actv pow, actv pow Q, lctomagntc momnt of momntum T, oto lp angula fquncy m and oto angl θ m may b computd by u of th popod mathmatcal modl of VSSU pow ccut and mthod of oluton: ( d d d d q q ) ( d d q d d q ) = 3, (0) Q = 3, ()

6 Tannt oc and Dynamc of Vaabl Spd ump Stoag Unt 249 m ( d d q ) T =.5 pl, (2) wh p th pol pa numb. m =, (3) θ m = m. (4) Th go output o conumd pow of th VSSU dpnd on potntal wat pow [3, 4]: 3 = kg H, (5) wh k th popotonalty facto, H th pu hght and G th poton of th dflcton whl. Condng th potntal wat pow th pow of th hydolctc gnato may b dtmnd n tm of mchancal wat pow fo gnato opaton: g =, (6) 2 g ( p) = αgg βgg γ g wh α g, β g and γ g a th coffcnt of th functon computd by th mthod of lat qua. Th pow of th pump th functon of mchancal wat pow fo gnato pow g < 0% : = 0, p 2 p( p) = αp p βp p γp, (7) wh α p, β p and γ p a th coffcnt of th functon computd by th mthod of lat qua. By ung functon (6) and (7) dpndnc of th mchancal hydaulc tubn pow on th angula fquncy a tablhd fo gnato and pump opaton (Fg. 2). Th dpndnc of th man paamt of th hydaulc tubn pow on th angula fquncy (Fg. 2) a follow: maxmum wat pow g max and p max, mnmum wat pow g mn and p mn, avag wat pow g avg and p avg, maxmum angula pd of th tubn g max and p max, mnmum angula pd of th tubn g mn and p mn (ach of thm paatly dtmnd und gnato and pump opaton condton). Th mchancal momnt of momntum T m may b found a follow fo gnato opaton: T m(g) g g( g) =, (8)

7 250 Rmanta ana Dkny, Dau Alšauka p, g pmax g max pavg p p p mn p g g avg g mn g, p g mn p mn g = p = g max p max Fg. 2. Dpndnc of th hydaulc tubn pow on th angula fquncy. and mlaly fo th pump on: T m(p) p( p) =. (9) Maxmum pow g max and p max und gnato and pump opaton condton a lmtd by pu hght H. Mnmum pow g mn and p mn fo th copondng opaton a lmtd by th tchncal paamt of th hydaulc tubn. Avag pow of th hydaulc tubn g avg and p avg may b calculatd by man of dpndnc hown n Fg. 2 fo angula fquncy = = pu. Th tuctu of th xct contol ytm mut b compod fo th popod mathmatcal modl of th VSSU pow ccut and functon of th ytm lmnt mut b matchd wth th paamt of th pow ccut.

8 Tannt oc and Dynamc of Vaabl Spd ump Stoag Unt Stuctu of xct contol ytm Th tuctu of th VSSU xct contol ytm nclud th am contol lmnt wth th am mathmatcal dfnton a that of th xct contol ytm of ynchonou hydolctc unt. Wth fnc to th xct contol ytm tuctu of a ynchonou gnato and wnd pow taton wth aynchonou machn, a modfd tuctu of mathmatcal modl lmnt of th VSSU xct contol ytm may b contuctd [5]. Mathmatcal contol lmnt mantan tabl convt and nvt cunt and voltag lvl to nu th ytm tablty (Fg. 3). Th xct contol ytm tuctu dagam cont of cunt, voltag, actv and actv pow and fquncy ynchonzng contoll, a wll a of maudquantty tanfomaton componnt wth compnaton flt xcutng popotonalntgatng (I) and popotonalntgatngdffntatng (ID) functon (Fg. 4). Functon tuctu compng fdback btwn oto and tato pow ccut and mchancal componnt of th hydaulc tubn and dflcton whl ntact and nu th labl opaton of th VSSU xct contol ytm, th opaton bng matchd wth th lctcal pow ytm. T u Q m Rgulato of actv and actv pow Rgulato of oto cunt and voltag Q E Rgulato of actv pow and dct voltag Rgulato of tato cunt and voltag u Q Tanfomaton block Q u Tanfomaton block Modulaton Invt θ m Dmodulaton E Convt C E θ Tz θ Rgulato of fquncy f VSSU ow ytm T Tubn Gat G θ m θ Rgulato of tubn T m Fg. 3. Stuctu dagam of an xct contol ytm.

9 252 Rmanta ana Dkny, Dau Alšauka max u max I t T 2 E t T 5 ' I t T ' mn ' max mn T 3 Σ T 4 u mn K K p Σ ' u mn ' u max Contoll of convt and nvt K c Fg. 4. Mathmatcal modl of a mplfd xct contol ytm. Th popod mathmatcal modl of th VSSU xct contol ytm tuctu nabl on to valuat popt of th VSSU gnato and pump opaton and to pfom a mathmatcal mulaton of tannt poc. Th man paamt of th mathmatcal modl (Fg. 4) dcbng th tuctu of th xct contol ytm a th followng: tm contant T () T (5), ntgaton facto K, popotonalty facto K p, compnaton facto K c, tanfomd oto o tato cunt I t, tanfomd ummay cunt I ' t, tanfomd oto o tato voltag E t, maxmum cunt lmt ' max and max, mnmum cunt lmt ' mn and mn, maxmum voltag lmt u ' max and ' u max, mnmum voltag lmt u mn and u mn. Thotcal ach pfomd n accodanc wth popod mathmatcal modl of VSSU pow ccut and xct contol ytm. 4. Rach ult Smulaton hav bn cad out on th VSSU of 250 MW atd pow, wth a 00 m pu hght. Aft matchng mathmatcal modl of VSSU pow ccut and xct contol ytm wth hydolctc paamt of th tubn, th ntal condton fo tadytat gnato and pump opaton a dtmnd. Th balanc of actv and actv pow n th lctcal pow ytm mantand f th avag actv pow of VSSU g avg = 78 MW fo coγ = 0.8 und gnato opaton condton and p avg =200 MW fo coγ = 0.9 und pump opatng condton. Intal condton and th lmt of th mathmatcal modl oluton convgnc a dtmnd n accodanc wth th opaton condton of VSSU. ow flow vaaton valuatd by applyng th NwtonRaphon mthod and th nflunc of th vaaton to th VSSU opaton condton condd tablhd. Fo th pupo th actv pow vaaton n th lctcal pow ytm load qual to ± of

10 Tannt oc and Dynamc of Vaabl Spd ump Stoag Unt 253 VSSU atd pow mtatd. Th tm dpndnc of angula fquncy m of th oto lp, cunt I t, actv pow and actv pow Q copondng to th gnato and pump opaton (Fg. 5 8, a and b, pctvly) a dtmnd fo th tm ntval t =, ung th dgtal ntgaton mthod. a) Gnato Slp, pu Tm, c.00 Slp, pu b) ump gm Tm, c Fg. 5. Gaphc of th tm dpndnc of oto lp..00 If th angula fquncy of th oto lp bng vad at a at of.2 %/m n th ntval btwn 0% and 6% und gnato opaton condton, actv pow may b changd n th ntval btwn 0 and 50 MW (Fg 5, a). Und gnato opaton condton om acclaton of th cunt and actv pow vaaton may b ognatd by th mchancal pow of wat whch may cau th hydaulc hock (Fg. 6, a and 7, a). Th acclaton contolld by gulato of cunt and voltag n th oto ccut ung th cocton of oto angula fquncy by changng tm contant. Th at of dpndnc vaaton (Fg. 5 8) dtmnd n a 0. tm ntval. Th at dtmn th poblty of VSSU pow contol und gnato and pump opaton condton. Th maxmum at of actv pow vaaton copondng to th VSSU gnato opaton 28 MW/m (Fg. 7, a), th maxmum at of actv

11 254 Rmanta ana Dkny, Dau Alšauka pow vaaton 7 Mva/m (Fg. 8, a), accodngly, th valu of maxmum cunt vaaton at 0.7 ka/m (Fg. 6, a). Cunt, A a) Gnato gm Tm, c 500 b) ump gm 000 Cunt, A Tm, c Fg. 6. Gaphc of th tm dpndnc of cunt. If th angula fquncy of th oto lp bng vad at a at of 2.0 %/m n th ntval ±6% und pump opaton condton, th actv pow may b changd n th ntval btwn 0 and 00 MW (Fg 5, b). Th maxmum at of actv pow vaaton copondng to th VSSU pump opaton 33 MW/m (Fg. 7, b), th maxmum at of actv pow vaaton 3 Mva/m (Fg. 8, b), accodngly, th valu of maxmum cunt vaaton at.4 ka/m (Fg. 6, b). Compaon of gnato and pump opaton how that th pump opaton of VSSU mo pfabl fo th mo contnuou pfomanc du to th fact that th ntvty of loadd hydaulc tubn gulato to th mchancal acton and hydaulc hock und pump opaton condton low than that und gnato opaton condton.

12 Tannt oc and Dynamc of Vaabl Spd ump Stoag Unt a) Gnato gm Actv pow, MW Tm, c Actv pow, MW b) ump gm Tm, c Fg. 7. Gaphc of th tm dpndnc of actv pow. 0 a) Gnato gm Ractv pow, Mva Tm, c.00 Ractv pow, Mva b) ump gm Tm, c Fg. 8. Gaphc of th tm dpndnc of actv pow.

13 256 Rmanta ana Dkny, Dau Alšauka 5. Concluon. A mathmatcal modl of th vaabl pd pump toag unt contuctd and computaton a pfomd. 2. Th actv pow of a 250 MW vaabl pd pump toag unt may b changd at a at of 28 MW/m und gnato opaton condton, and at a at of 33 MW/m und pump opaton condton. An ffctv contol of th actv pow n th lctcal pow ytm and mall fquncy dvaton may b nud und ngy gnaton and conumpton condton. 3. Th actv pow of th vaabl pd pump toag unt may b changd at a at of 7 Mva/m und gnato opaton condton and at a at of 3 Mva/m und pump opaton condton. Ractv pow dmand n th lctcal pow ytm may b atfd and hgh voltag qualty may b nud. 4. Th maxmum pobl actv pow chang of 50 MW may b achd dung 6.5 m und gnato opaton condton, and th copondng chang of 00 MW may b achvd dung 3.0 m whn th unt opat a a pump. 5. Th vaabl pd pump toag unt may b ud fo ffctv pow contol wth a tabl opaton whn th vaaton of th oto angula fquncy n th ntval of fom 0% to 6% n pct of ynchonou fquncy und gnato opaton condton and n th ntval ±6% und pump opaton condton. REFERENCES. MdvdvaTšnobvaja, V., Attka, R., Tammoja, H. Chaacttc numb of pmay contol n th olatd Etonan pow ytm. Ol Shal, 20, 28(2S), Suul, J. A., Uhln, K., Undland, T. Vaabl pd pumpd toag hydopow fo ntgaton of wnd ngy n olatd gd ca dcpton and contol tatg. oc. Nodc Wokhop on ow and Indutal Elctonc, NORIE/2008, Jun 9, 2008, Epoo, Fnland, 8 pp. 3. Lung, J.K., Lu, Y., Hung, W.L., Kao, W.S. Modlng and dynamc mulaton of doubly fd adjutablpd pumpd toag unt. IEEE T. Engy Conv., 2007, 22(2), Nagua, O., Hguch, M., Tan, K., Oyak, T. Htach adjutablpd pumpdtoag ytm contbutng to pvnton of global wamng. Htach Rvw, 200, 59(3), Takahah, R., Tamua, J., Tada, Y., Kuta, A. Modl dvaton of an adjutabl pd gnato and t xctaton contol ytm. 4 th ow Sytm Computaton Confnc (SCC), Jun 2002, Svll, Span,, Rcvd Octob 24, 202

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