Phase Shift Transformers Modelling
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1 Phase Shift Trasformers Modellig ersio:.. CGMES v.. 8 May ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
2 Phase Shift Trasformers Modellig Cotets Cotets.... troductio.... Mappig to CM classes ad attributes.... Reactace formulas summary table Symmetrical Phase shifters Oe phase diagram ad equatios Expressio of the agle ad ratio per tap Expressio of the equivalet series reactace give the agle Three-phase diagrams Quadrature booster Oe phase diagram ad equatios Expressio of the agle ad ratio per tap Expressio of the equivalet series reactace give the agle Three-phase diagrams Asymmetrical Phase Shifter Oe phase diagram ad equatios Expressio of the agle ad ratio per tap Expressio of the equivalet series reactace give the agle Three-phase diagram phase trasformer ad symmetrical phase shifter Oe phase diagram ad equatios Expressio of the agle ad ratio per tap Expressio of the equivalet series reactace give the agle ad the i-phase trasformer ratio Techology priciples phase trasformer ad asymmetrical phase shifter Oe phase diagram ad equatios Expressio of the agle ad ratio per tap Expressio of the equivalet series reactace give the agle ad the i-phase trasformer ratio Techology priciples Appedix Symmetrical Phase Shifters with two cores Quadrature boosters Quadrature booster with two cores Quadrature booster with a sigle core... ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
3 Phase Shift Trasformers Modellig 9.5. Asymmetrical phase shifter Asymmetrical phase shifter with two cores Asymmetrical phase shifter with a sigle core phase trasformer ad asymmetrical phase shifter... 6 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
4 Phase Shift Trasformers Modellig. troductio This documet describes Phase-Shiftig Trasformer (PST modellig accordig to the type ad techology of the equipmet; ad more specifically, equivalet series reactace of phase shifters i the positive sequece as a fuctio of the phase shift agle. these specific models, the resistaces ad the magetizig currets are always eglected. This documet also provides the mappig betwee the equatios for each type ad techology of PST to the CM classes ad attributes which are icluded i the ENTSO-E Commo Grid Model Exchage Stadard (CGMES versio... Mappig to CM classes ad attributes To illustrate how to use the PST modellig described i this documet, the mappig to CM 6 classes is preseted i the followig table: PST type Geeral Case Symmetrical phase shifters Asymmetrical phase shifter -phase trasformer ad symmetrical phase shifter -phase trasformer ad asymmetrical phase shifter CM class cim:phasetapchagertabular cim:phasetapchagersymmetrical or cim:phasetapchagerliear cim:phasetapchagerasymmetrical cim:phasetapchagersymmetrical ad cim:ratiotapchager cim:phasetapchagersymmetrical ad cim:ratiotapchager Recommedatio t is highly recommeded to use tabular data to exchage PST parameters (cim:phasetapchagertabular istead of havig to recalculate the parameters per tap accordig to each model type PST attribute CM attribute cim:phasetapchagertablepoit.step cim:tapchager.eutralstep u r cim:phasetapchagernoliear.voltagestepcremet cim:tapchagertablepoit.ratio cim:phasetapchagertablepoit.agle cim:phasetapchagerliear.stepphaseshiftcremet ( cim:tapchagertablepoit.x ( cim:phasetapchagerliear.xmi or ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
5 Phase Shift Trasformers Modellig cim:phasetapchagernoliear.xmi ( cim:phasetapchagerliear.xmax or cim:phasetapchagernoliear.xmax cim:phasetapchagerasymmetrical.widigcoectioagle. Reactace formulas summary table Equipmet type Symmetrical Phase Equivalet series reactace as a fuctio of the phase shift agle shifters ( ( ( Asymmetrical Phase si / ( si / Shifter ( ( ( ( -phase trasformer ad symmetrical phase shifter -phase trasformer ad asymmetrical phase shifter ( r, ( r, ( r r ta ta si ta cos si ta cos r si / r ( ( ( r om om r r r om om ( ta si ta ( r cos ( ta ( si ta cos r si / with ( r A ta ad ( r om r om r ta si si ta cos cos ariable Meaig Maximal phase shift: the imum agle value of the phase shifter agles table r Nomial ratio of the i-phase trasformer om Maximal phase shift whe the i-phase trasformer ratio is omial 5 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
6 Phase Shift Trasformers Modellig. Symmetrical Phase shifters.. Oe phase diagram ad equatios e ( ' si e e e (.. Expressio of the agle ad ratio per tap Based o the figure above: ( ( or ta u A r.. Expressio of the equivalet series reactace give the agle Assumig the reactace of the regulatig widig varies as the square of the umber of turs, the equivalet reactace ca be writte as follows for o delta-hexagoal techologies (see proof i appedix 9.: si / ( ( ( ( si / parameters: : imal phase shift (: equivalet series reactace at zero phase shift ( : equivalet series reactace at imal phase shift variable: : curret phase shift The formula above is valid for sigle or double core symmetrical phase shifters except for the hexagoal techology. For sigle core symmetrical phase shifters: (= 6 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
7 Ohm Phase Shift Trasformers Modellig mpedace 5k symmetrical double core phase shifter (i Ohm measurmets from field test theoretical law phase shift agle (degree.. Three-phase diagrams Dual core: Sigle core: a b c a b c a a b c a b c a a b c a b c a a b c a b c a b c a b c a b c a a c a b c a c Shut trasformer Series trasformer 7 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
8 Phase Shift Trasformers Modellig Sigle core, delta hexagoal: a b c a b c a a b c a b c a b c a c 5. Quadrature booster 5.. Oe phase diagram ad equatios e ( ta e ' e ( ad vary with.cos = costat. 5.. Expressio of the agle ad ratio per tap Based o the figure above: Ata ( u r ( u 8 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
9 Phase Shift Trasformers Modellig 5.. Expressio of the equivalet series reactace give the agle Assumig the reactace of the regulatig widig varies as the square of the umber of turs, the equivalet reactace of the quadrature booster ca be writte as follows (see proof i appedix 9.: ( ( ( ta ( ta parameters: : imal phase shift (: equivalet series reactace at zero phase shift ( : equivalet series reactace at imal phase shift variable: : curret phase shift For quadrature boosters with a sigle core: (= 5.. Three-phase diagrams Dual core: Sigle core: a b c a b c a a b c a b c a a b c a b c a a b c a b c a b c a b c a b c a a c a b c a c Shut trasformer Series trasformer 9 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
10 Phase Shift Trasformers Modellig 6. Asymmetrical Phase Shifter 6.. Oe phase diagram ad equatios e ( ta ' e. e. e ( si ta cos is fixed, oly ad vary. 6.. Expressio of the agle ad ratio per tap Based o the figure above: ( u si A ta ( u cos r ( u si ( u si 6.. Expressio of the equivalet series reactace give the agle Assumig the reactace of the regulatig widig varies as the square of the umber of turs, the equivalet reactace ca be writte as follows (see proof i appedix 9.5: ( ( ( ta ( ta si ta cos si ta cos parameters: : imal phase shift ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
11 Phase Shift Trasformers Modellig (: equivalet series reactace at zero phase shift ( : equivalet series reactace at imal phase shift : boost voltage agle variable: : curret phase shift 6.. Three-phase diagram Dual core: a b c a a b c a a b c a b c a b c WNDNGS CONNECTONS a b c a a c Shut trasformer Series trasformer 7. -phase trasformer ad symmetrical phase shifter 7.. Oe phase diagram ad equatios r e (r, e (. ' r. si e e ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
12 Phase Shift Trasformers Modellig r ad vary, ad =r 7.. Expressio of the agle ad ratio per tap Same as. with the additio of the i-phase trasformer ratio r. 7.. Expressio of the equivalet series reactace give the agle ad the iphase trasformer ratio Assumig: the reactace of the regulatig widig varies as the square of the umber of turs, the equivalet reactace is the sum of the reactace of the i-phase trasformer r ad the reactace of the phase shifter part, the phase shiftig agle does ot deped o the i-phase ratio r The equivalet reactace ca be writte as follows (ot proved: ( r, r r si / r ( ( ( om r om si / 6 Parameters: r om : omial ratio of the i-phase trasformer r (r om : equivalet series reactace of the i-phase trasformer at omial i-phase ratio : imal phase shift (: equivalet series reactace of the phase shifter part at zero phase shift ( : equivalet series reactace of the phase shifter part at imal phase shift at omial iphase ratio (r om ariables: r: curret ratio of the i-phase trasformer : curret phase shift 7.. Techology priciples No example foud. ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
13 Phase Shift Trasformers Modellig 8. -phase trasformer ad asymmetrical phase shifter 8.. Oe phase diagram ad equatios e (r, r r (r ta ' r e. e si ta cos is fixed, oly r ad are variables, varies as a cosequece. (. e 8.. Expressio of the agle ad ratio per tap Not proved. 8.. Expressio of the equivalet series reactace give the agle ad the iphase trasformer ratio Assumig: the reactace of the regulatig widig varies as the square of the umber of turs, the equivalet reactace is the sum of the reactace of the i-phase trasformer r ad the reactace of the phase shifter part, The equivalet series reactace ca be writte as follows (ot proved: r r ( ( ( ta si ta ( rcos ( r, ta ( si ta cos r om rom r ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
14 Phase Shift Trasformers Modellig with si ( r A ta with ( rom r si ta cos cos r om ta 6 Parameters: r om : omial ratio of the i-phase trasformer r (r om : equivalet series reactace of the i-phase trasformer at omial i-phase ratio r om : fix boost voltage agle ( r : imal phase shift for omial i-phase ratio (r om om (: equivalet series reactace of the phase shifter part at zero phase shift ( : equivalet series reactace of the phase shifter part at imal phase shift at omial iphase ratio (r om ariables: r: curret ratio of the i-phase trasformer : curret phase shift For = / (quadrature booster: rom ( r Ata ta r 8.. Techology priciples -phase regulatig auto-trasformer Series trasformer Switchig etwork Shut autotrasformer The phase shift regulatio may be o the shut or o the series trasformer ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
15 Phase Shift Trasformers Modellig 9. Appedix 9.. Symmetrical Phase Shifters with two cores R Detailed three phase diagram Z/, / turs A Z/, / turs A Ai Ai A Ao Ao Bi Bi B Bo Bo Ci Ci C Co Co Z, turs A /.A B C Ai-Ao Bi-Bo Ci-Co C-B A-C B-A A B C Series Trasformer AY /. AY Z, turs Z, turs Shut Trasformer Oly varies. 5 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
16 Phase Shift Trasformers Modellig Example of umerical values: = =8 =68 =8 =, =8,6 = Expressio of the output curret o ad the shut curret =i-o: Whe cosiderig a ideal phase shifter, the coservatio of the electric power is writte: * * Si ii oo As the voltage agle is shifted by alpha: o e i The curret agle must also be shifted by alpha as well: o e i The, the shut curret i o ( e i Expressio of the shut equivalet reactace The shut reactace shut( is defied as the equivalet reactace which crossed by the series iput curret (i would produce the reactive losses of the shut trasformer: Qshut. shut (. i with: Qshut.... / i e ( cos i si( shut ( si( / Hypothesis: The shut ( si / Expressio of the equivalet series reactace The series reactace series( is defied as the equivalet reactace which crossed by the series iput curret (i would produce the reactive losses of the series trasformer: Qseries. series (. i with: Qseries.. i.. o.. 6 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
17 Phase Shift Trasformers Modellig ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu 7 as see previously: i e o series trasformer curret relatioship:... o i the i e ad cos ( i e i the / si( ( cos ( ( series / si( ( series Expressio of the total equivalet reactace / si ( or / si / si ( ( ( ( with: ( / si ( ( Remark: oly varies.
18 Phase Shift Trasformers Modellig 9.. Quadrature boosters 9.. Quadrature booster with two cores Detailed three phase diagram a b c a a b c a a b c a b c a b c a b c a a c Shut trasformer Series trasformer For each physical value (= or a a with a b c a e shut trasformer with variable ratio / with reactace o the primary widig ad o the secodary widig: Y Y.. 8 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
19 Phase Shift Trasformers Modellig ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu 9 Hypothesis: the reactace varies like the square of the umber of turs : Series trasformer of fixed ratio / with reactace o the primary widig ad o the secodary widig: Lik betwee series ad shut trasformers: Primary widigs: Secodary widigs: ( a a a c b a ( a a c b a Calculatio:.... At o load coditios (=:.. Ad geometrically: ta hece ta ta
20 Phase Shift Trasformers Modellig.. ta ta Ad comes:.. with ( ( ( ( ta ta 9.. Quadrature booster with a sigle core Detailed three phase diagram a b c a b c a b c a a b c a b c a b c a c varies. ' ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
21 Phase Shift Trasformers Modellig ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu Assumig At o-load: Ad geometrically: ta hece ta ta ta ta ( ta ta ( (
22 Phase Shift Trasformers Modellig 9.5. Asymmetrical phase shifter 9.6. Asymmetrical phase shifter with two cores Detailed three phase diagram: a b c a a b c a a b c a b c =z. a b c a b c a a c Shut trasformer Series trasformer ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
23 Phase Shift Trasformers Modellig ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu For each physical value (= or c b a a a with e a shut trasformer equatios: Hypothesis: the reactace varies like the square of the k ratio: Series trasformer of fixed ratio k with series reactace o the primary widig: Lik betwee series ad shut trasformers: Primary widigs: z, a complex umber, determies the couplig betwee the series ad shut trasformer secodary widigs:. z a. z for a quadrature booster z Calculatio:.... z z.... z At o load coditios (=: z.... Ad geometrically: cos ta si ta. e
24 Phase Shift Trasformers Modellig hece Ad ta ta si ta cos si ta cos.. z ta ta si ta cos si ta cos comes:. z. ( ( ( with ta ( ta si ta cos si ta cos 9.7. Asymmetrical phase shifter with a sigle core a b c a b c a b c a a b c a b c =z. a b c a c ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
25 Phase Shift Trasformers Modellig Oly varies. ' z. z. z. Assumig z. At o-load: z. ta Ad geometrically: e. si ta cos hece ta ta si ta cos si ta cos ( ta si ta cos ta si ta cos ta si ta cos ( ( ta si ta cos 5 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
26 Phase Shift Trasformers Modellig phase trasformer ad asymmetrical phase shifter Examples of detailed three-phase diagrams: voltage regulatig auto-trasformer ad Quadrature booster: 6 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
27 Phase Shift Trasformers Modellig oltage regulatig auto-trasformer ad Quadrature booster: EH widig H widig E voltage regulatig widig Phase shift regulatig widig 5 Tertiary widig 6 Primary widig of the series trasformer 7 Secodary widig of the series trasformer 7 ENTSO-E ASBL Aveue de Cortebergh Brussels Belgium Tel Fax ifo@etsoe.eu www. etsoe.eu
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