Session 3, Page /34 Acive Harmonic Filering and Reacive Power Conrol Imiaion Measured Currens: Define array of ime and define angular frequency: Δ Δ.3 4 s 86Hz 6 secδ ω 6Hz π6hz ω() ω Load curren as a funcion of ime I mag A I ampl I mag f 6Hz Sinusoidal harmonic erms for firs 5 harmonics of a square wave (magniude will be added laer): f A ( ) cos( πf) f 7A ( ) cos( π7f) f 3A ( ) cos( π3f) f 3A ( ) cos( π3f) f 9A ( ) cos( π9f) f 5A ( ) cos( π5f) f 5A ( ) cos( π5f) f A ( ) cos( πf) Harmonic ampliudes (assume hree phase, hyrisor recifier wih siff dc curren source, 3rd harmonic removed). Noe he negaive signs and 's: Noe since funcions are cosines, he paern of he signs changed a I ampl I ampl I ampl I ampl I ampl a 3 a 5 a 5 7 a 7 9 a a 3 a 3 5
Session 3, Page /34 Harmonic curren equaion: i loada () a f A () a 3 f 3A () a 5 f 5A () a 7 f 7A () a 9 f 9A () a f A () a 3 f 3A () a 5 f 5A () Creae degree phase shif in unis of ime. a ime a 36 6Hz ime 5.556 3 s i loadb () i loada a ime i loadc () i loada a ime Transform measured currens o he saionary dq () reference frame: θr() π 6.Hz Use equaions from he Clarke Transformaion as equaions insead of marix for now i ds () 3 i loada ( ).5i loadb ().5i loadc () i qs () i loadb () i loadc () 3 Q axis 8 ou of phase wih some definiions Park's Transformaion in Marix Form θ() ω synchronously roaing reference frame, noe ha his is generally shifed by / for roaing machines.
Session 3, Page 3/34 P () 3 cos( θ() ) sin( θ() ) cos θ() sin θ() Clarke Transform on he Currens π 3 π 3 cos θ() π 3 π sin θ() 3 I αβ () P( ) i loada () i loadb () i loadc () i loada () i loadb () i loadc ()..4.6.8.
Session 3, Page 4/34 Transformed volages (no ha i ds () in phase wih i a () i ds () i loada () i qs () I αβ () I αβ ()..4.6.8. Volage as a funcion of ime V mag 5kV ϕ 3deg v a () V mag cos( ω() ϕ) v b () V mag cos( ω() deg ϕ) v c () V mag cos( ω() deg ϕ)
Session 3, Page 5/34 Clarke Transformaion on Volages V αβ () P( ) v a () v b () v c () 3 4 4 V αβ () 4 V αβ () 4 4 3 4..4.6.8. Now calculae insananeous real and reacive power MW kw MVA MW MVAR MW
Session 3, Page 6/34 Phasor form firs: V a V mag e j3 deg I a I mag e j deg P 3ph 3Re V a I a P 3ph 3.897MW Q 3ph 3Im V a I a Q 3ph.5MW Noe: we need he 3/ erm because of /3 consan in ransformaion marix. P αβ () Q αβ () 3 V αβ () I αβ () V αβ () I αβ () V αβ () I αβ () 3 V αβ () I αβ () V αβ () I αβ () v α () V αβ () i α () I αβ () v β () V αβ () i β () I αβ () PQ αβ () 3 v α () v β () v β () v α () i α () i β () p () PQ αβ () q () PQ αβ ()
Session 3, Page 7/34 5 6 P 3ph 4 6 P αβ () p () 3 6 6 5 3..5
Session 3, Page 8/34 4 6 Q 3ph Q αβ () q () 3 6 6 6 5 3..5 In pracice, he average real and reacor power from he phasor calculaion won' be available. We we need some form of averaged o low pass filered value.. Half cycle averaged on he, resuls: p αβ () q αβ ().5 6Hz 6Hz = p.5 a d a P αβave () = p αβ () p αβ 6Hz = q.5 a d a Q αβave () = q αβ () q αβ.5 6Hz.5 6Hz. Low pass, averaging digial filer
Session 3, Page 9/34 RS 8 LP() RS p RS k Δ = LQ() RS k = RS k q RS k Δ RS For mos of his example we will sick wih jus he 3 phase complex power phasor soluions. Compensaor Currens: Case : Jus correcing harmonics: 3 i compαβ () v α () v β () v α () v β () v β () v α () p () P 3ph q () Q 3ph By subracing average P and Q, he error signal for he conrol group is jus he harmonic disorion in "insananeous P and Q" i compα () i compαβ () i compβ () i compαβ ()
Session 3, Page /34 5 i compα () i compβ () 5 5 3..5 I compabc () P( ) A i compα () i compβ () Noe ha he zero sequence par of he compensaor curren is assumed o be zero. This is due o he assumpion ha he compensaor is a 3 wire device (noe ha a VSC is inherenly ungrounded, so he converer opology needs o change o add a ground reurn and he abiliy o compensae zero sequence erms.
Session 3, Page /34 I compabc () 5 I compabc () I compabc () 5 5 3..5 Now find he compensaed currens: i sourcea () i loada () I compabc () i sourceb () i loadb () I compabc () i sourcec () i loadc () I compabc ()
Session 3, Page /34 v a () i sourcea () i sourceb () i sourcec ()..4 Noe ha v a () and i a () are no in phase
Session 3, Page 3/34 Case : This ime perform PF correcion and harmonic compensaion v 3 α () v β () i compαβ () p () P 3ph v α () v β () By subracing average P, bu no average Q, v β () v α () q () he error signal for he conrol group is boh he harmonic disorion in "insananeous P i and Q" and bringing he oal reacive power compα () i compαβ () o zero. i compβ () i compαβ () i compα () i compβ () 5 3..5
Session 3, Page 4/34 I compabc () P( ) A i compα () i compβ () I compabc () I compabc () I compabc () 5 3..5 Now find he compensaed currens: i sourcea () i loada () I compabc () i sourceb () i loadb () I compabc () i sourcec () i loadc () I compabc ()
Session 3, Page 5/34 v a () i sourcea () i sourceb () i sourcec ()..4 Noe ha v a () and i a () are in phase now. Uniy power facor. Case 3: PF correcion, load balancing and harmonics: Keep he same phase A load curren and mainain he same volages across he load as above. i loadb () i loada a ime i loadc () A Effecively only have a load conneced from phase A o phase B
Session 3, Page 6/34 I αβ () P( ) i loada () i loadb () i loadc () v α () V αβ () v β () V αβ () i α () I αβ () i β () I αβ () i () I αβ () PQ αβ () 3 v α () v β () v β () v α () i α () i β () p () PQ αβ () q () PQ αβ () Now we need o calculae average power RS 8 LP() RS k p RS k Δ RS
Session 3, Page 7/34 i compαβ () v 3 α () v β () p ( ) LP() v α () v β () By subracing average P, bu no average Q, v β () v α () q () he error signal for he conrol group is boh he harmonic disorion in "insananeous P () and Q" and bringing he oal reacive power o zero. The negaive sequence curren associaed i compα () i compαβ i compβ () i compαβ () wih he unbalance also produces oscillaions in p() and q(). The conrol algorihm brings he oscillaing erm o zero. Effecively balancing he phase currens. i compα () i compβ () 5 3..5
Session 3, Page 8/34 I compabc () P( ) A i compα () i compβ () I compabc () I compabc () I compabc () 5 3..5
Session 3, Page 9/34 Now find he compensaed currens: i sourcea () i loada () I compabc () i sourceb () i loadb () I compabc () i sourcec () i loadc () I compabc () v a () i sourcea () i sourceb () i sourcec ()..4 Noe ha currens are balanced, v a () and i a () are in phase now. Uniy power facor.
Session 3, Page /34 Power sysem: VSC
Session 3, Page /34 Alpha-Bea TRANFORMATION F T *6Hz PI * WREF 3 T VAF VBF VCF K + + + - x y VALPHA x y T VSA K VAF VBF VCF + - x y x y VBETA T VSB K VBF VSC K VCF 3 SWITA SWITB SWITC T K + + + - x y x y IALPHA T SWITB SWITC + - x y x y IBETA T
Session 3, Page /34
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Session 3, Page 5/34 Case : Harmonic compensaion Phase A load curren 5 5-5 - -5.5.4.55.7.85. (file af_swiching.pl4; x-var ) c:swita-busa
Session 3, Page 6/34 Compensaor curren 7. [A] 5.5 35. 7.5. -7.5-35. -5.5-7..5.4.55.7.85 [s]. (file af_swiching.pl4; x-var ) c:ifilta-busa
Session 3, Page 7/34 Commanded curren and filer curren 7. 5.5 35. 7.5. -7.5-35. -5.5-7..5.4.55.7.85 [s]. (file af_swiching.pl4; x-var ) c:ifilta-busa : IFILTA facors: offses: -
Session 3, Page 8/34 P and Q a he load -.5 * 6-3. -3.5-4. -4.5-5.. 5. 4. 5 5. 7. 8 5 [s ]. (file a f_ s w ic h in g.p l4 ; x -v a r ) : P 3 P H : P A V E. * 6 -.5 -. -.5 -. -.5-3. -3.5-4..5.4.55.7.85 [s]. (file a f_ s w ic h in g.p l4 ; x-va r ) : Q 3 P H : Q A V E
Session 3, Page 9/34 Filered Curren and phase A volage 5. 87.5 5. 6.5. -6.5-5. -87.5-5..5.4.55.7.85 [s]. (file af_swiching.pl4; x-var ) c:vsa -VSLA v:vsa facors:. offses: Angle of VSA = degrees Angle of curren VSA-VSLA = 9.56 degrees
Session 3, Page 3/34 Filered Curren Harmonic Specrum. MC's PloXY - Fourier char(s). Copying dae: 3/9/7 File af_swiching.pl4 Variable c:vsa -VSLA [rms] Iniial Time:.3833 Final Time:.4 [A] 8 6 4 5 5 5 5 3 harmonic order - 5 5 5 3 harmonic order Curren oal harmonic disorion =.69 %
Session 3, Page 3/34 Case : Harmonic and power facor compensaion Only Change: Q3PH + - ZERO QLF T Compensaor curren [A] 8 4-4 -8 -.5.4.55.7.85 [s]. (file af_swiching.pl4; x-var ) c:ifilta-busa
Session 3, Page 3/34 Commanded curren and filer curren 8 5 - -4-7.5.4.55.7.85. (file af_swiching.pl4; x-var ) facors: offses: : IFILTA c:ifilta-busa -
Session 3, Page 33/34 Filered Curren and phase A volage 5. 87.5 5. 6.5. -6.5-5. -87.5-5..5.4.55.7.85 [s]. (file af_swiching_pfcorrec.pl4; x-var ) c:vsa -VSLA v:vsa facors: offses:. Angle of VSA = degrees Angle of curren VSA-VSLA = 9.5 degrees
Session 3, Page 34/34 MC's PloXY - Fourier char(s). Copying dae: 3/9/7 File af_swiching_pfcorrec.pl4 Variable c:vsa -VSLA [rms] Iniial Time:.3833 Final Time:.4 [A] 78 56 34-5 5 5 3 harmonic order - - 5 5 5 3 harmonic order Curren THD = 7.9% Compromise wih rying o do reacive compensaion and harmonic compensaion