Allenbach, P.

Avellan, F.

Hérou, J.-J.

Nicolet, C.

Sapin, A.

Simond, J.-J.

Infoscience - École polytechnique fédérale de Lausanne

 "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;<   $$t= ';ter;atio;al @eeti;g of t=e "orB #roup o;  THE BEHAVI)UR )F HYDRAULIC MACHINERY UNDER STEADY )SCILLAT)RY C)NDITI)NS  Stuttgart, :ermany   TRANSIENT PHEN)MENA IN FRANCIS TURBINE P)@ER PLANTSA INTERACTI)N @ITH THE P)@ER NET@)RK  Christophe NICOLET Prof. François AVELLAN EPFL / Laboratory for Hydraulic Machines,  Lausanne, Switzerland Philippe ALLENBACH Dr. Alain SAPIN Prof. Jean-Jacques SIMOND EPFL / Electrical Machines Laboratory,  Lausanne, Switzerland  Dr. Jean-Jacques HEROU EDF / Centre d’Ingénierie Hydraulique Le Bourget-du-lac, France ABSTRACT @odels of =<drauli. .o:po;e;ts 1ased o; i:peda;.e :et=od =aFe 1ee; i:ple:e;ted i; a softGare .alled H6'@6INKL M=is softGare alloGs t=e si:ulta;eous solutio; of t=e ele.tri.al% =<drauli.% :e.=a;i. a;d .o;trol eNuatio;s e;suri;g a proper i;tera.tio; 1etGee; t=ese four parts of a s<ste:L Osi;g t=is tool% i; t=is paper% t=e tra;sie;t 1e=aFior of a; isla;ded poGer ;etGorB is i;FestigatedL M=is ;etGorB .o:prises a * Pra;.is tur1i;es =<droele.tri. poGer statio; of $Q* @"% a ;u.lear poGer statio; of $,++ @" a;d a .o;su:er loadL M=e ;u.lear poGer statio; :odeli;g taBes i;to a..ou;t t=e rotati;g :asses a;d stiff;ess% t=e rotatio;al speed regulators% a first order stea: tur1i;e :odel a;d t=e ge;eratorL MGo distur1a;.es are si:ulated usi;g 6'@6INR t=e =<droele.tri. poGer pla;t sGit.= off a;d t=e load a..epta;.e a;d reSe.tio;L M=e si:ulatio; results s=oG =oG t=e poGer is 1ala;.ed duri;g su.= tra;sie;tsL M=is approa.= alloGs for t=e a;al<sis of .o;trol .o::a;d para:eters of a; isla;ded poGer ;etGorBL N)MENCLATURE Term Symbol Definition Term Symbol Definition TieUo:etri. =ead ) ) V U W pXY!gZ [:] )<drauli. resista;.e ( ( V (]L d^ [sX:*] PloG rate _ [:,Xs] )<drauli. i;du.ta;.e ` ` V `]Ld^ [s*X:*] "aFe speed a [:Xs] )<drauli. .apa.ita;.e a a V a]L d^ [:*] aross se.tio; area & [:*] (ated =ead = = V )X)( Pri.tio; fa.tor " [5] (ated torNue # # V MX M( [5] 6i;gular losses b [5] 6tati. tur1i;e $ $ V ta;5$Y%X &Z "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< Term Symbol Definition Term Symbol Definition .oeffi.ie;t .=ara.teristi. Ile.tri.al resista;.e (e [o=:] (ated floG % % V _X_( [5] Ile.tri.al i;du.ta;.e `e [)] (ated rotati;g speed & & V 'X'( [5] Ile.tri.al .apa.ita;.e ae [P] ce;sit< ! [bgX:,] (otati;g speed ' [radXs] @e.=a;i.al i;ertia ' [bgL:*] MorNue M [N:] #uide Fa;e ope;i;g degree < [5] M=er:al ti:e .o;sta;t !t= [s] (egulator statis: 1p [d] INTR)DUCTI)N M=e operatio; of a; =<droele.tri. poGer pla;t is su1Se.t to seFeral tra;sie;t p=e;o:e;o; due to group star5up a;d s=ut5doG;% :odifi.atio; of operati;g poi;t% eart= fault% out of p=ase s<;.=ro;iUatio; duri;g start5up% e:erge;.< stop a;d so o;L & full :odel of t=e poGer pla;t taBi;g i;to a..ou;t t=e =<drauli.% ele.tri.% :e.=a;i.al a;d .o;trol deFi.e .o:po;e;ts is reNuested to i;Festigate all t=e Gorst .ases a;d to .al.ulate .o;trol .o::a;d para:eters e;suri;g operati;g sta1ilit<L M=e ITP` `a1orator< for Ile.tri.al @a.=i;es e`@Ie =as deFeloped a softGare .alled 6'@6IN Y(efL f% (efL $+Z for t=e si:ulatio; of ele.tri.al poGer ;etGorBs s<ste:s i; tra;sie;t or stead< state :odes a;d adSusta1le speed driFe s<ste:sL Mo 1e a1le to stud< t=e d<;a:i. 1e=aFior of a G=ole =<droele.tri. poGer pla;t i;.ludi;g ele.tri.al% =<drauli. a;d .o;trol .o:po;e;ts% a =<drauli. e^te;sio; =as 1ee; deFeloped a;d i:ple:e;ted i; 6'@6IN Y(efL g a;d ZL M=is deFelop:e;t is t=e result of t=e .olla1oratio; 1etGee; t=e `@I a;d t=e ITP` `a1orator< for )<drauli. @a.=i;esL M=e e^te;sio; i;.ludes t=e :odels of pipe% FalFe% surge ta;B a;d Pra;.is tur1i;eL Mo :at.= t=e for:alis: of t=is softGare t=e i:peda;.e :et=od Y(efL $% (efL h a;d (efL $$Z =as ;aturall< 1ee; .=ose; for t=e :odeli;g of t=e =<drauli. .o:po;e;tsL M=us% t=e .orrespo;di;g goFer;i;g eNuatio;s .a; 1e i:ple:e;ted easil< a;d t=e =<drauli. e^te;sio; 1e;efits fro: t=e ar1itrar< topolog< feature alloGi;g to :odel .o:ple^ pipi;g s<ste:sL M=e :odeli;g of t=e =<drauli. .o:po;e;ts is prese;ted i; Ma1le $L (efL QTreFious si:ulatio;s alread< de:o;strated t=e i:porta;.e of full< taBi;g i;to a..ou;t t=e =<drauli. a;d ele.tri.al part of a poGer s<ste: Y(efL 4ZL M=is paper e:p=asiUes t=e ;eed of a detailed :odeli;g i; t=e .ase of tra;sie;t 1e=aFior si:ulatio;s of a; isla;ded poGer ;etGorBL & ;etGorB .o:prisi;g a =<droele.tri. poGer statio;% a ;u.lear poGer statio; a;d a .o;su:er load is :odeledL ToGer 1ala;.e is a;al<Ued duri;gXafter =<droele.tri. poGer pla;t sGit.= off a;d .o;su:er load Fariatio;sL            $,L$+L*++, *    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< Component Electrical eJuiKalent EJuation set 1 22c cdH dHdx g A C (a dt dt(! ! " " # 11 122Rdx (H (DgA$% " " R(       2 2Ld( d(dxH LgA dt dt% " "      & ' ccocpccpc (gA(KHH 22"#     ccc (dtdHzA ")(     copcc gALL "      22)( ()*+,"BW 22)( ()+,"hWH  & '1tan (+ )#"  -"IIt dxxgAL)(1  Table 1 Modeling of the hydraulic components using impedance method. R/2 Lh/2 Lh/2 C Rh R/2 H1 Hc Q1 Q2 H2 Datum. Q2 Q1 D, a,  $dx H1 H2 Rv & '22 ( ) ( )vv vd G(H (g C s A s% "Rv Qv s 0 1 Datum"Hv Hydraulic grade line Qv "Hv Hc Datum WH = WH(.,Q,y)  Lt Rt HtQ Hc Q1 Q2 Hpc  Qc Rc Lc Cc HRc HLc Hydraulic grade line Rc Ac(z) Kpc Qc Cc Aco LpcQ1 Q2 Hpc  IHt + HrI-1 Tm , # Iy Datum $,L$+L*++, ,    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< CASE STUDY  M=e s<ste: i;Festigated is a **+ BV isla;ded poGer ;etGorB .o:prisi;g a * Pra;.is tur1i;e =<droele.tri. poGer pla;t% a ;u.lear poGer pla;t a;d a .o;su:er :odeled as a; (` Faria1le load YPigure $ZL )<droele.tri. u;it sGit.= off a;d load reSe.tio; a;d a..epta;.e o; t=is isla;ded ;etGorB is i;Festigated 1< si:ulati;g t=e tra;sie;t 1e=aFior of t=e e;tire s<ste:L ';tera.tio;s 1etGee; t=e =<droele.tri. poGer pla;t a;d t=e rest of t=e s<ste: are prese;tedL  2 1 1 Figure 1 Modeling of the power plant with SIMSEN.  Hydraulic power plant modeling M=e =<droele.tri. poGer pla;t .o:prises a ta;B% a galler<% a surge ta;B% * Pra;.is tur1i;es of 4g @" a;d * ge;eratorsL M=e data .orrespo;di;g to =<drauli. poGer pla;t of t=is e^a:ple are prese;ted i; Ma1le * a;d t=e .=ara.teristi. .urFes of t=e tur1i;es are prese;ted i; Pigure * Git= 6utter represe;tatio; Y(efL jZL M=e rotati;g :asses of t=e ge;erator a;d t=e tur1i;e are .o;;e.ted .o;sideri;g t=e stiff;ess of t=e s=aftL #aller< 6urge Ma;B Tipe Mur1i;es #e;erators ` V h+++ : c V $+ : " V +L+, a V $+++ :Xs &YUkQQZ V Q++ :* &YQQkUk4QZ V  h++ :* &YUl4QZ V Q++ :* ` V $*j : c V jLj : " V +L+*  a V $*j+ :Xs )t( V 4* : ;( V *++ rp: _t( V $$h :,Xs Mt( V hL$$e g N:'tWg V $LQgQeg bg:* 6; V f4 @V& O; V $QLj BV Tole pairs V $j P; V j+ )U Table 2 Characteristics of the power plant. M=e triSu;.tio;% G=i.= distri1utes t=e floG rate to t=e tur1i;es% is :odeled 1< t=ree si;gular losses para:eteriUed usi;g a .oeffi.ie;t fu;.tio; of t=e t=e floG rate repartitio; 1etGee; t=e t=ree 1ra;.=esL M=e losses .oeffi.ie;ts are taBe; fro: (efL ,L  T'c .o;trollers are used forR - output Foltage regulatio; a.ti;g o; field Foltage of t=e s<;.=ro;ous ge;eratorsm - rotatio;al speed regulatio; a.ti;g o; t=e guide Fa;e ope;i;g degree of Pra;.is tur1i;eL  $,L$+L*++, h    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;<  < R ope;i;g degree < R ope;i;g degree Figure 2 Characteristics WB and WH of the turbines. Nuclear power plant modeling M=e ;u.lear poGer pla;t is .o;stituted of t=ree h,, @" stea: tur1i;es Ya =ig= pressure tur1i;e Y)T$Z a;d tGo loG pressure tur1i;es Y`T$%*ZZ .o;;e.ted to a $h++ @V& ge;erator YPigure ,Z L M=e rotati;g speed of t=e h :asses s=aft is $j++ rp:L M=e h rotati;g :asses a;d , .o;;e.ti;g  stiff;ess :odel is taBe; fro: (efL * a;d su::ariUed i; Pigure hL M=e torNue of t=e stea: tur1i;es is :odeled 1< a first order tra;sfer fu;.tio; taBi;g i;to a..ou;t t=e proportio;al regulatio; Git= a statis: bp a;d a t=er:al ti:e .o;sta;t !t= as des.ri1ed i; Pigure jL M=e set of para:eters of t=e tra;sfer fu;.tio; is prese;ted i; Ma1le ,L '; additio;% t=e stea: tra;sit ti:e fro: t=e =ig= pressure tur1i;e to t=e loG pressure tur1i;e t=roug= t=e re5=eaters% is taBe; i;to a..ou;t 1< a ti:e dela<R G(z) = z-bL M=e si:ulatio; results of a rotatio;al speed set poi;t .=a;ge is prese;ted i; Pigure gL &lt=oug= t=is operatio; is ;ot realisti.% it is used i; order to illustrate t=e d<;a:i. respo;se of t=e u;itL   Figure 3 Model of the nuclear power plant. $,L$+L*++, j    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< Model of the shaft+L++IW++jL++IW+g$L++IW+Q$Lj+IW+Q*L++IW+Q*Lj+IW+Q,L++IW+Q,Lj+IW+QhL++IW+Q+ * h g 4Element S';ertia [Bgn:*]+L++IW++jL++IW+h$L++IW+j$Lj+IW+j*L++IW+j*Lj+IW+jstiff;ess [BN:Xrad]stiff;essi;ertia  Figure 4 ';ertia a;d stiff;ess of t=e ;u.lear poGer pla;t rotati;g s=aft Y(efL *ZL 11th s/ ! ,T#s% &!bp#s% ) !c#s%+#1&bp% K-!#s%  ( ) 1( )( ) ( ) 1bp thT sG s Ks s s. . /" " !# ! , Figure 5 Mra;sfer fu;.tio; of t=e proportio;al regulator of t=e stea: tur1i;e i;.ludi;g t=er:al ti:e .o;sta;t (t=L   "th VsW bp V%W b VsW HP1 +Lj h + LP1,2 $j $* ,L4 Table 3 Tara:eters of t=e stea: tur1i;es :odelsL  nLP1,2/nnucn TLP1,2/Tnucn THP1/Tnucn b 30 sFigure 6 c<;a:i. respo;se of t=e ;u.lear u;it to a .=a;ge of t=e rotatio;al speed set poi;t fro: +LjL;; to ;;L $,L$+L*++, g    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< L)AD PERTURBATI)N Hydroelectric units switch off M=e first i;Festigatio; .o;.er;s t=e trippi;g of t=e =<dro5ge;erators G=ere t=e .ir.uit51reaBer 1etGee; t=e tra;sfor:er a;d t=e ge;erator are sGit.=ed off YY$Z i; Pigure $Z% G=ile t=e poGer set poi;t of t=e ;u.lear u;it re:ai;s .o;sta;tL 6i:ulta;eousl<% t=e distri1utor of t=e tGo Pra;.is tur1i;es are .losed li;earl< i; Q se.o;dsL M=e eFolutio; of t=e :ai; Faria1les duri;g a;d after t=e total load reSe.tio; is prese;ted i; Pigure Q a;d Pigure 4L T/TR Turbine 1 Surge tank inlet discharge \st/\tot n/nR Turbine 1Surge tank leKel z/Htot Turbine 1 inlet piezometric head H/Htot Figure 7 Evolution of the main variables of the hydroelectric power plant during the switch off  of the two hydraulic turbines.    y/yma_ Hinlet/Htot \st/\tot \t/\R n/nR T/TR z/Htot Figure 8 Evolution of the hydraulic turbine 1 variables during the switch off.  $,L$+L*++, Q    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< &t t=e outset% t=e ele.tro:ag;eti. torNue of t=e ge;erators drops to Uero i;sta;ta;eousl<% as a .o;seNue;.e t=e rotatio;al speed of t=e groups i;.reaseL M=e .losure of t=e distri1utor redu.es t=e =<drauli. torNue Nui.Bl<% li:iti;g t=e rotatio;al speedL M=e distri1utor .losure i;du.es a "ater=a::er effe.t i; t=e addu.tio; part of t=e poGer pla;t a;d a :ass os.illatio; 1etGee; t=e reserFoir a;d t=e surge ta;BL @oreoFer% t=e effe.t of ;o;5u;ifor: surge ta;B .ross5se.tio; is properl< taBe; i;to a..ou;tL M=e ele.tro:ag;eti. torNue drop of t=e =<dro5ge;erators i;du.es a rotatio;al speed di:i;utio; of t=e ;u.lear u;it G=i.= .o:pe;sates partiall< t=e la.B of poGer o; t=e ;etGorBL )oGeFer% due to t=e proportio;al stru.ture of t=e rotatio;al speed regulatio;% t=e ;o:i;al speed is ;ot re.oFered after t=e tra;sie;t as s=oG; i; Pigure fL oe.ause t=e poGer ;etGorB is ;ot i;ter.o;;e.ted% t=e ;o:i;al freNue;.< of j+ )U .ould ;ot 1e re.oFered Git=out .=a;gi;g t=e poGer set poi;tL   THP1/Tnucn TLP1,2/Tnucn nLP1,2/nnucn Temanuc/TnucFigure 9 c<;a:i. respo;se of t=e ;u.lear u;it due to =<dro u;it sGit.= offL  Load recection and acceptance M=e se.o;d i;Festigatio; is t=e si:ulatio; of t=e tra;sie;t 1e=aFior of t=e G=ole s<ste: due to a su..essiFe i;.rease a;d de.rease of t=e .o;su:er load YY*Z i; Pigure $ZL M=e eFolutio; of t=e poGer at t=e .o;su:er load is prese;ted i; Pigure $+L M=e d<;a:i. respo;se of t=e =<dro u;its a;d t=e ;u.lear u;it are prese;ted i; Pigure $$ a;d Pigure $*L \RLaload PRLaload  Figure 10 ToGer Fariatio; of t=e (` load :odeli;g t=e .o;su:erL $,L$+L*++, 4    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;<  HT1ainlet/HR nT1/nR \T1/\R TT1/TR y/yma_ Figure 11 c<;a:i. respo;se of t=e =<drauli. tur1i;e $ due to t=e su..essiFe load reSe.tio; a;d a..epta;.eL  TemT1/TRTemT2/TRnT1,2,nuc/nR Temanuc/Tnucan  Figure 12 Ile.tro:ag;eti. torNue of t=e * =<dro u;its a;d of t=e ;u.lear u;it duri;g  t=e su..essiFe load reSe.tio; a;d a..epta;.eL M=e de.rease of ,d of t=e load i;du.es a rotatio;al speed i;.rease of all t=e u;itsL M=e rotatio;al speed regulators of t=e =<drauli. tur1i;es a.t Nui.Bl< o; t=e Gi.Bet gate to redu.e t=e torNueL &fter *+ se.o;ds t=e rotatio;al speed error is redu.ed to $LL M=e ;u.lear u;it rea.ts i; t=e sa:e ti:e spa; 1ut re.oFers its ;o:i;al poGer leFel after * :i;utesm G=e; t=e hj @" load Fariatio; is full< .o:pe;sated 1< t=e =<dro u;itsL M=e d<;a:i. respo;se of t=e s<ste: is si:ilar G=e; t=e load i;.reasesL )oGeFer% t=e first tra;sie;t =as i;du.ed a :ass os.illatio; 1etGee; t=e reserFoir a;d t=e surge ta;B a;d t=is affe.ts t=e =ead at t=e tur1i;e i;let redu.i;g t=e :a^i:u: poGer of t=e tur1i;esL M=is si:ulatio; s=oGs .learl< =oG t=e poGer 1ala;.ed is affe.ted i; su.= a s:all ;etGorB duri;g tra;sie;tsL "=e; t=e load .=a;ges% all u;its a.t to .o:pe;sate t=e rotatio;al speed Fariatio;% 1ut G=e; stead< state $,L$+L*++, f    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< .o;ditio;s are re.oFered% t=e poGer .=a;ge is a1sor1ed 1< t=e =<drauli. u;its G=ile ;u.lear u;it does ;ot .=a;ge its poGer leFelL  C)NCLUSI)N & tra;sie;t 1e=aFior due to load pertur1atio;s i; a; isla;ded poGer ;etGorB =as 1ee; i;FestigatedL M=e ;etGorB is .o:prisi;g a * Pra;.is tur1i;es =<droele.tri. poGer pla;t% a ;u.lear poGer pla;t a;d a .o;su:er :odeled as a (` loadL Pirst% t=e :odeli;g of t=e =<droele.tri. poGer pla;t% 1ased o; t=e i:peda;.e :et=od% is des.ri1edL M=e;% t=e :odeli;g of t=e ;u.lear poGer pla;t taBi;g i;to a..ou;t t=e rotati;g :asses a;d t=e stiff;ess of t=e s=aft% t=e proportio;al regulators% a first order tra;sfer fu;.tio; for stea: tur1i;es a;d t=e ge;erator is prese;tedL M=e si:ulatio; of t=e tra;sie;t 1e=aFior of t=e G=ole isla;ded ;etGorB =as 1ee; perfor:ed usi;g t=e softGare 6'@6INL MGo distur1a;.e .ases =aFe 1ee; si:ulatedR a * =<droele.tri. u;its sGit.= off a;d a load reSe.tio; a;d a..epta;.eL M=e si:ulatio; results of t=e =<droele.tri. poGer pla;t sGit.= off e^=i1its a de.rease of t=e ;etGorB freNue;.< G=ile t=e =<droele.tri. u;its are affe.ted 1< Gater=a::er a;d :ass os.illatio;s effe.tsL M=e si:ulatio; of t=e su..essiFe load reSe.tio; a;d a..epta;.e s=oG t=at 1ot= poGer statio;s% =<drauli. a;d ;u.lear% a.ts to Beep t=e ;etGorB freNue;.< .o;sta;tL )oGeFer% G=e; stead< state .o;ditio;s are re.oFered% t=e poGer Fariatio; is proFided 1< t=e =<drauli. poGer pla;t G=ile t=e ;u.lear statio; re:ai;s at its preFious poGer leFelL M=e opti:iUatio; of t=e .o;trol .o::a;d para:eters a;d a sta1ilit< assess:e;t of a; isla;ded ;etGorB reNuire :odeli;g properl< eFer< poGer sour.e to stud< t=e ;etGorB freNue;.< flu.tuatio;sL "it= a; eNuiFale;t sour.e i;stead of a detailed :odel% it Gould ;ot 1e possi1le to perfor: su.= a; a;al<sisL  ACKN)@LED:MENTS "e Ga;t to t=a;B si;.erel< Nadi;e TaSea;5"asso;g a;d `aure;t oellet fro: IcP5a') a;d crL Mu pua; fro: ITP`5`@I for t=eir .olla1oratio; i; t=e deFelop:e;t p=aseL REFERENCES (efL $ P-p% qL &L% $f4f% HMra;sie;t floG i; pipes% ope; .=a;;els a;d seGersKL Illis )orGood `i:ited% a=i.=esterL (efL * #--6IN% qL% 6'@-Nc% qL5qL% 6MI'#`IcI(% b% 6-ININ% `L% 6MIPPIN6% qL5aL% 6MOooI% qLm H6eFeral aspe.ts of t=e torsio;al fatigue da:age of tur1o5group s=afts due to ele.tri.al distur1a;.esKL &L'L@L `irge% $f4j% g,L$5g,L$+L (efL , 'cI`sa'b% 'L I% $fgf% t@u:e;to des pertes de .=argeL aoeffi.ie;ts de perte de .=arge si;gulirres et de pertes de .=arge par frotte:e;t tL Taris R I<rollesL (efL h q&I#I(% aL% $fQQ% tPluid tra;sie;ts i; =<dro5ele.tri. e;gi;eeri;g pra.ti.e tL #lasgoGR ola.BieL (efL j @&(a)&`% @L% P`I6) #L &Nc 6OMI( TL% $fgj% HM=e aal.ulatio; of "ater=a::er pro1le:s 1< @ea;s of t=e cigital ao:puterKL Tro.L ';tL 6<:pL "ater=a::er Tu:ped 6torage TroSe.ts% &6@I% a=i.agoL $,L$+L*++, $+    "# $% &'() *++,  -.to1er 45$+% *++,% 6tuttgart% #er:a;< $,L$+L*++, $$   (efL g N'a-`IM% aL% &VI``&N% PL% T(IN&M% qL IL% 6&T'N% &L% 6'@-Nc% qL qL% *++$% t& ;eG tool for t=e si:ulatio; of d<;a:i. 1e=aFiour of =<droele.tri. poGer pla;ts tL $+t= ';ter;atio;al :eeti;g of t=e GorB group o; t=e 1e=aFiour of =<drauli. :a.=i;er< u;der stead< os.illator< .o;ditio;s% Mro;d=ei:% NorGa<% qu;e *g5*4 *++$L (efL Q N'a-`IM% aL % &``INo&a)% TL % 6&T'N% &L % 6'@-Nc% qL5qL % &VI``&N% PL m *++*%  tNeG Mools for t=e 6i:ulatio; of Mra;sie;t T=e;o:e;a i; Pra;.is Mur1i;e ToGer Tla;ts tL Tro.eedi;gs of t=e *$st '&)( 6<:posiu: o; )<drauli. @a.=i;er< a;d 6<ste:s% `ausa;;e% 6GitUerla;d% f5$* 6epte:1er *++*% ppL j$f5j*4L  (efL 4 N'a-`IM% a=ristop=e% &VI``&N% Pra;vois% &``INo&a)% T=ilippe% 6&T'N% &lai;% 6'@-Nc% qea; qa.Nues% bV'a'N6bw% 6o;ia% a(&)&N% @ar.usm t6i:ulatio; of Mra;sie;t T=e;o:e;a i; Pra;.is Mur1i;e ToGer Tla;ts R )<droele.tri. ';tera.tio; tL Tro.eedi;gs of "aterpoGer p'''% &dFa;.i;g Me.=;olog< for 6ustai;a1le I;erg<% ouffalo% NLwL% O6&% qul< *++,L (efL f 6&T'N% &L% $ffj% H`ogi.iel :odulaire pour la si:ulatio; et l]utude des s<str:es d]e;trax;e:e;t et des ruseau^ ule.triNuesKL T=c t=esis% ITP`% M=ese ;y$,hgL (efL $+ 6'@-Nc% qL5qL% 6&T'N &L% &``INo&a) TL% *++*% 6i:ulatio; des ruseau^ et des s<str:es dse;trax;e:e;ts ule.triNuesL oulleti; 6IVXV6I *++* NrLQL (efL $$ "w`'I% IL oL z 6M(IIMI(% VL`L% $ff,% HPluid tra;sie;ts i; s<ste:sKL Tre;ti.e )all% I;gleGood aliffs% NLqL 

Transient Phenomena in Francis Turbine Power Plants: Interaction with the Power Network.

http://infoscience.epfl.ch/record/131119/files/tpiftppiiwtpn_AIRH_workgroup.pdf

Transient Phenomena in Francis Turbine Power Plants: Interaction with the Power Network.

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