DC-bus Voltage Controllers for a Three-Phase Voltage-Source Inverter for Distributed Generation

Transcription

1 European Associaion for he Developmen of Renewable Energies, Environmen and Power Qualiy Inernaional Conference on Renewable Energies, and Power Qualiy (ICREPQ9) Valencia (Spain), 5h o 7h April, 29 DC-bus Volage Conrollers for a Three-Phase Volage-Source Inverer for Disribued Generaion Bar Meersman, Ber Renders, ieven Degrooe, Tine Vandoorn and ieven Vandevelde Elecrical Energy aboraory (EEAB), Deparmen of Elecrical Energy, Sysems and Auomaion (EESA), Ghen Universiy, Sin-Pieersnieuwsraa 4, B-9 Ghen, Belgium, Phone: , Fax: Bar.Meersman@UGen.be Absrac An imporan funcion of he bus volage conroller of volage-source inverers (VSI) for disribued generaion (DG) applicaions is o conrol he balance beween ac and dc power. Neverheless is he bus volage conroller no he criical par of he conrol of he VSI. Therefore i is jusified ha lile aenion is paid o he design of his bus volage conroller wha can be seen in lieraure. However, his conroller can (negaively) influence he behaviour of he VSI. In hree-phase sysems a ripple can exis in he bus volage due o unbalance or harmonics presen in he grid volage or curren. This ripple can inerac wih he bus volage conroller which can have negaive consequences on he injeced curren. Also he iming of updaing he oupu of he bus volage conroller can have consequences on he waveform disorion which can resul in oscillaions. In his paper he focus is on he iming of updaing. An overview of hree possible bus volage conrollers is given. The response of he differen implemenaions of dc-bus volage conrollers during a ransien is simulaed. Keywords model, digial conrol, hree phase volage-source inverer (VSI), disribued generaion, neural-poin-clamped VSI. Inroducion An imporan funcion of he dc-bus volage conroller of VSI for DG applicaions is o conrol he balance beween he power a he grid-side and he power a he dc side. The dc-bus volage conroller oupus he fundamenal inpu conducance which resuls in he reference curren. The bus volage conroller is no he criical par of he conrol of he VSI because balancing he inpu and oupu power is a slow process and he (large) capacior a he dc-bus serves as a buffer. Therefore i is jusified ha lile aenion is paid o he design of his bus volage conroller which can be seen in lieraure [?, 9]. However his conroller can (negaively) influence he behaviour of he VSI. For hree-phase sysems under symmeric operaion (hreephase symmerical volage and curren) here is no ripple a he dc-bus volage as opposed o single-phase sysems where a ripple a double grid frequency exiss. If an unbalance (in volage or curren) or harmonics are presen in a hree-phase sysem, a ripple occurs a he dc-bus volage. This ripple can inerac wih he bus volage conroller if i was no designed o handle a disorion in he dc-bus volage []. The ineracion can resul in harmonics in he injeced curren. The bus volage conroller is usually a PI-conroller wih a randomly chosen sample frequency [2], [ 4]. The sample frequency is usually chosen low in order o reduce he effec of ripple on he bus volage. By choosing a low sample frequency he response of he bus volage conroller will also be slow. This can resul in high over- or undervolages of he bus volage in case of severe fauls. Anoher mehod o improve he ripple rejecion is o sample a he zero-crossings of he ripple. By doing so he ripple becomes a hidden oscillaion for he bus volage conroller [5]. In [6] and [7] a low pass filer is used o filer ou he ripple. Adding a low pass filer degrades he ransien response of he dc-bus volage conrol and causes a larger variaion of dc-bus volage in he ransien sae. Anoher aspec of he bus volage conroller is he iming of updaing he oupu. The oupu of he bus volage conroller can be synchronised wih he zero-crossings of a phase volage [?, 9]. This mehod will resul in a sep in he ampliude in he oher wo phases of he injeced curren if he oupu is changed due o a ransien in he power balance. This sep in he ampliude will negaively influence he grid volage. This can be prevened by changing he iming of updaing he oupu of he bus volage conroller. A balance has o be found beween he reacion speed of he bus volage conroller and he resisance agains variaions of bus volage on he bus volage conroller. Increasing he reacion speed by increasing he sample and updae frequency of he bus volage conroller can lead o harmonics in he injeced curren in case of unbalance or harmonics in he grid volage or curren. The iming of updaing he oupu of he bus volage conroller can also be imporan. In he following he emphasis will be placed on he iming of updaing. This paper will address hree differen bus volage conrollers:

2 Hz bus volage conroller Hz bus volage conroller wih delayed updaes a he zero-crossing of he grid volage khz bus volage conroller The advanages and disadvanages of he differen bus volage conrollers will be given. The ransien behaviour of hese hree bus volage conrollers will also be sudied. 2. The Volage Source Inverer There are wo possibiliies o inerface he DG conneced inverer o a hree-phase four-wire sysem, which is ypically he opology of a low-volage disribuion nework. One possibiliy is o have a hree-wire inverer which is conneced o he four-wire sysem by means of a /Y g isolaion ransformer. Since he isolaion ransformer is heavy and expensive, i is no desired in many applicaions. The second possibiliy is using a ransformerless four-wire inverer. There are generally wo ypes of four-wire inverer opologies: hree-leg wih spli dc bus and four-leg. The hreephase hree-leg inverer wih spli dc-bus enables o implemen a hree-phase four-wire sysem wih a neural poin. Compared o a hree-phase hree-wire sysem, i does no require he isolaion ransformer o creae a neural poin and i provides hree-dimensional conrol. Compared o a hree-phase four-leg opology, i saves wo power swiches and also reduces conrol complexiy. A disadvanage of his opology is ha he dc-bus capaciors have o be oversized because harmonic curren can flow hrough hese capaciors ino he neural wire. Fig. depics he opology of he hree-phase neural-poin clamped volage-source inverer. The hree-phase hree-leg inverer has a spli dc-bus where he op and boom halves of he dc-bus are assumed o be evenly disribued such ha half of he dc-bus volage is over each capacior. The dc-bus can be energized by a (small) DG-uni, like fuel cells, phoovolaic devices and wind urbines. The inverer oupus are conneced o a hree-phase second order -C filer which aenuaes high frequency componens resuling from swiching. S S 3 S 5 dc-bus volage conroller provides he balance beween he ac and he dc-bus power. The oupu of he bus volage conroller is he fundamenal inpu conducance g a he ac-side of he inverer. The inpu conducance is muliplied wih he fundamenal componen of he grid volage which resuls in he reference curren. By doing so, he inverer provides a sinusoidal curren. The phase angle of he fundamenal componen of he grid volage is obained by using a Phase ocked oop (P). The design of he curren conroller is based on he Z- domain model of he inverer insead of he frequenly used aplace-domain model. The sampling of he signals and he dynamics of he pulse-wih modulaor are more accuraely described by using a Z-model which resuls in a beer conroller. The bandwih of he curren conroller is 2 khz which allows o rack he 5 Hz reference curren perfecly. The oupu of he curren conroller is added o he oupu of he duy-raio feed-forward. The duy-raio feed-forward branch is added o obain a beer disurbance rejecion [8]. The resul of his summaion is he inpu of he PWM modulaor which oupus he swiching-signals for he inverer. vdc v dc i,a v g,a i,b P Volage conroller v g g,b i,b P i,c vg,c v g,b, g i,c P v g,c, g i,a v g,a, Curren conroller Duy-raio feedforward Curren conroller Duy-raio feedforward Curren conroller Duy-raio feedforward d 2 d 4 PWM d 6 δ 6 Figure 2: Conrol sraegy for he hree-phase neuralpoin-clamped volage-source inverer 4. Theoreical Model δ 2 δ 4 V g,a V g,b V g,c n i,a i,b i,c S 2 A S 4 B S 6 C 2 C dc 2 C dc N V dc 2 V dc 2 V dc In order o design he volage conroller, he ransfer funcion of he inpu conducance o he oupu volage has o be derived. This ransfer funcion enables o design he oupu volage conroller in he Z-domain. Fig. 3 depics he model which is used o derive he ransfer funcion of he inpu conducance o he oupu volage. The insananeous power p () is given by: Figure : Topology of he hree phase neural-poinclamped volage-source inverer 3. The Conrol Sraegy The conrol sraegy for he hree-phase neural-poinclamped volage-source inverer is depiced in Fig. 2. The p () = v g,a () i,a () 2 v g,b () i,b () 2 v g,c () i,c () 2 di 2,a () di 2,b () di 2,c () ()

3 V g,a V g,b V g,c p () n i,a () i,b () i,c () η p 2() V dc N p dc () Figure 3: Model o derive he ransfer funcion of he inpu conducance o he oupu volage The dc-power is given by: p 2 () = p dc () C dc 2 dv 2 dc () The relaionship beween inpu and oupu power is given by: p () = η p 2 () (3) where η is he efficiency of he inverer. I can be assumed ha he zero sequence componen of he injeced curren is very small which resuls in ha he power in he neural can be negleced. The conrol sraegy which is used (cf Fig. 2) validaes he assumpion ha he zero sequence componen of he injeced curren can be negleced. I is assumed ha he curren conrol works perfecly, such ha he following relaionship can be jusified: (2) i,x () g () v g,x () (4) wih x= phase a, b or c. Equaions () (4) resul in he following differenial equaion: g () vg,a() 2 d(g () v g,a ()) 2 2 g () vg,b() 2 d(g () v g,b ()) 2 2 g () vg,c() 2 d(g () v g,c ()) 2 2 = η p dc () η C dc dvdc 2 () 2 In small-signal analysis each variable can be wrien as he summaion of he seady-sae value and a small excursion from his seady-sae: v g,x =V g,x ˆv g,x v dc =V dc ˆv dc g =G ĝ. i,x =I g,x î g,x p dc =P dc ˆp dc where capials are used for seady-sae values and haed small leers for small excursions from seady-sae. The grid volage in phase a, V g,a (), in seady-sae can be wrien as: V g,a () = 2 V g,rms sin(ω ) (6) (5) where V g,rms is he rms-value of he nominal ampliude of he grid volage. The small signal equaion of (5) is obained by subracing he equilibrium of equaion (3) wih equaion (5) which resuls in: 2 G [V g,a () ˆv g,a () V g,b () ˆv g,b () V g,c () ˆv g,c ()] 3 Vg,rms 2 ĝ () 6 2 G Vg,rms 2 dĝ () 2 2 G2 V g,a () dˆv g,a() 2 2 G2 V g,b () dˆv g,b() G 2 ˆv g,a () dv g,a() 2 2 G2 V g,c () dˆv g,c() G 2 ˆv g,b () dv g,b() G 2 ˆv g,c () dv g,c() = η ˆp dc () η C dc d(v dc () ˆv dc ()) A ripple on he bus volage can cause he bus volage conroller o injec a curren conaining harmonics. In order o avoid his, he bandwih of he volage conroller is se low. Averaging equaion (7) over one period of he grid volage is jusified because he bandwih of he volage conroller is small (25 - Hz). When he bandwih is larger, his averaging is no longer jusified. The resuling equaion will hen have erms in ˆv g,a (), ˆv g,b () and ˆv g,c () which are disurbances for he process inpu conducance o he oupu volage. When uning a bus volage conroller having a larger bandwih, care should be aken ha he phase margin of he PI conroller is large enough such ha he process is sable under all condiions. The averaging of equaion (7) over one period of he grid volage resuls in he eliminaion of he erms in V g,x (): 3 Vg,rms 2 ĝ () 6 2 G Vg,rms 2 dĝ () d(v dc () ˆv dc ()) = η ˆp dc () η C dc In he aplace domain, equaion (8) can be wrien as: (7) (8) ˆv dc (s) = 3 V g 2 (s G ) ĝ (s) s η C dc V dc ˆp dc (s) (9) s η C dc V dc This resuls in he ransfer funcion of he inpu conducance o he oupu volage (in per uni): ˆv # dc (s) ĝ # (s) = 3 V g 2 s G η C dc V dc Vdc ref Zref s () The zero s = /( G ) can be negleced because i is siuaed a very high frequency (5 khz) compared o he desired bandwih of he oupu volage conroller (25 - Hz). By neglecing his zero, he ransfer funcion of he inpu conducance o oupu volage (in per uni) can be wrien as: ˆv # dc (s) ĝ # (s) = 3 V g 2 sηc dc V dc Vdc ref Zref τ v s ()

4 wih τ v = ηc dcv dc V ref dc Zref 3V 2 g (2) The open loop ransfer funcion of he oupu volage conroller in he Z-domain can now be wrien as: G o (z) = T b,v 2 τ v z z (z ) (3) where T b,v is he sample period of he oupu volage conroller. This ransfer funcion can be used o une he PI-conroller of he bus volage conroller. The sep response of he bus volage conroller is opimised by uning he PI-conroller using Sisoool in Malab. 5. The DC-bus Volage Conroller In he following secion an overview of he differen bus volage conrollers is given. In order o es he differen bus volage conrollers, he following experimen is done. A =22 ms he DG power is reduced from 2 kw o 66 W during 4 ms. A =26 ms he DG power is resored o kw. A. Hz bus volage conroller A firs possibiliy for a bus volage conroller is he Hz bus volage conroller. This bus volage conroller samples he bus volage a a frequency of Hz. The oupu of his conroller is updaed every ms and is synchronized wih he zero-crossings of he fundamenal volage of phase a. The curren of phase a is changed a he zero-crossings in order o minimize he waveform disorion due o he updaes of g a he zero-crossings [5]. When he oupu of he bus volage conroller changes due o a ransien in he power balance, here will be a sep in he curren of phase b and c which may resul in oscillaions. These oscillaions can become significan if he grid has a low resisance. Fig. 4 depics he response of he bus volage conroller during he es. A sep in he curren in phase b and c can be seen. The oscillaions caused by he sep in he curren resul in a disored curren. The low frequency of he volage conroller ( Hz) resuls in a slow response and in high over- or undervolages of he bus volage in case of severe fauls. B. Hz bus volage conroller wih delayed updaes a he zero-crossing of he grid volage To improve he bus volage conroller of A.. The reference value for he curren in every phase is updaed wih he zero-crossings of he respecive fundamenal volage. So when he inpu conducance changes, he reference values of he curren in phase a, b and c will alernaively be updaed. This has a beneficial effec on he curren waveform. In conras o he bus volage conroller of A. here will be no disorion in he curren. Fig. 5 depics he response of he bus volage conroller during he experimenal es. I can be seen ha here are vg() ig() vdc() (a) The grid volage.95.9 (b) The grid curren.85 (c) The bus volage Figure 4: The grid volage, grid curren and bus volage using he classical Hz bus volage conroller. A =22 ms he DG power is reduced from 2 kw o 66 W during 4 ms. no seps in he reference currens in conras o Fig. 4. The changes in ampliude a he zero-crossings can be noiced in Fig. 5(b). The sample frequency of he bus volage conroller wih delayed updaes is he same as he sample frequency of he bus volage conroller of A., namely Hz. The response of he presen volage conroller will no be faser in case of severe fauls. C. khz bus volage conroller A hird possibliy is he khz bus volage conroller. This conroller akes samples of he bus volage a a frequency of khz. The oupu of he volage conroller is also updaed a khz. Fig. 6 depics he response of he bus volage conroller during he experimenal es. In Fig. 6(b) i can be seen ha here are oscillaions in he curren caused by a sep in he reference curren. This bus volage conroller has a fas response bu is sensiive o disorions in he bus volage caused by harmonics or unbalance in he grid []. An oscillaion in he bus volage can resul in he inroducion of unwaned harmonics in he curren.

5 vg() (a) The grid volage vg() (a) The grid volage ig() - (b) The grid curren ig().4.2 vdc() (b) The grid curren.85 (c) The bus volage Figure 5: The grid volage, grid curren and bus volage using he Hz bus volage conroller wih delayed updaes a he zero-crossing of he grid volage. A =22 ms he DG power is reduced from 2 kw o 66 W during 4 ms. 6. Conclusion An imporan funcion of he bus volage conroller of volage-source inverers for disribued generaion applicaions is o conrol he balance beween he ac and he dc power. In hree-phase sysems a ripple can exis in he bus volage due o unbalance or harmonics presen in he grid volage or curren. This ripple can inerac wih he bus volage conroller which can have negaive consequences for he injeced curren. In case of severe fauls he bus volage conroller has o be able o reac fas so high underand overvolages are avoided. The iming of updaing he oupu of he bus volage conroller is also imporan because i can have consequences on he waveform disorion. In his paper he focus is on he iming of updaing. A overview of hree differen bus volage conroller implemenaions is given and heir response on a sudden ransien is simulaed. The Hz bus volage conroller has a low bandwih, such ha he volage conroller does no respond o a double frequency ripple which can be presen in he bus volage. However his bus volage conroller has a slow response so severe fauls can lead o high under- or overvolages. During ransiens here will be a sep in he curren vdc() (c) The bus volage Figure 6: The grid volage, grid curren and bus volage using he khz bus volage conroller. A =22 ms he DG power is reduced from 2 kw o 66 W during 4 ms. which may resul in oscillaions. These oscillaions can become significan if he grid has a low resisance. The second bus volage conroller is he Hz bus volage conroller wih delayed updaes a he zero-crossing of he grid volage which also has a low bandwih and a slow response in case of severe fauls. The delayed updaes a he zero-crossing of he grid volage resul in a disorion-free curren so here will no be oscillaions in he grid curren. The hird and las bus volage conroller is he khz bus volage conroller which has a high bandwih. This resuls in a fas response in case of fauls. An unbalance or harmonics in he grid volage or curren will resul in harmonic componens in he injeced curren because he bus volage conroller will reac on he ripple in he bus volage. Each bus volage conroller has advanages and disadvanages and he opimal conroller will differ depending on he applicaion.

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