Single-Phase voltage-source inverter TUTORIAL. Single-Phase voltage-source inverter

Transcription

1 TUTORIAL SnglePhae oltageource nerter

2 Th tutoral ntended to how how SmartCtrl can be appled to degn a generc control ytem. In th cae, a nglephae oltageource nerter wll ere a an example to demontrate the SmartCtrl capablte to degn multpleloop tructure. Along the tutoral, eeral apect wll be hghlghted: The SmartCtrl Equaton Edtor module can be appled to deelop mall gnal model for the power conerter (plant), current and oltage enor, etc. Th a ery eay to ue tool that allow the uer to operate tranfer functon (complex functon n nature) a mple arable of an equaton. Any text edtor can be ued to wrte the text code contanng the model. In addton, The Equaton Edtor module proded wth t own text edtor, wth ome yntax example to eae the model generaton procedure. The teadytate alue, plant and enor tranfer functon for both loop can be tored n the ame text code and, along the degn proce, end to the degn enronment the tranfer functon requred for each partcular loop. In the degn proce, t ery ueful to ue ome tranfer functon of the nner loop to degn the outer loop. SmartCtrl nclude a powerful mport / export functon that allow the uer to ualze n the degn enronment, at any tme; any tranfer functon that mght be requred. Dgtal control nherent delay can be condered at any tme jut by clckng on the correpondng con. No manual degn needed, t only needed the pecfcaton of the amplng frequency, bt number, etc and SmartCtrl wll compute the delay and how the correpondng Bode plot, a well a the compenator dgtal coeffcent. The tutoral tructured a follow: Frtly, a mple theoretcal ntroducton, regardng the doubleloop control of a nglephae oltageource nerter, proded. Accordng to th theoretcal model, the complete text code gen n ANNEX A. Once the procedure to degn both loop ha been hown, ome PSIM mulaton are proded to how the effect of the ue of the feedforward control acton. 2

3 The propoed control tructure for the nglephae oltageource nerter hown n Fgure L L O V DC DC n C C Load O L O PWM modulator Current enor Voltage enor Voltage enor con L ag DCm Inner Current Loop I L ref nt O m R V O med O ref V O ref p Fgure : Snglephae oltage ource nerter wth double control loop tructure The man pecfcaton are the followng: S NOM = 5 kva Nomnal apparent power V DC m = 400 V, DC nput oltage. V O rm = 230 V, Reference rm output oltage f = 50Hz; Output oltage frequency The nerter ue a unpolar PWM modulaton wth 0 khz carrer frequency. The output LC flter component are: L = 200 H RL = 00 m (Inductor equalent ere retance) C = 33 F. RC = 0 m (Capactor equalent ere retance) The oltage enor parameter are: Gan: = 0/500 = 0.02 Cutoff frequency = 3 khz The current enor parameter are: Gan: = 0/40 = 0.25 Cutoff frequency = 3 khz 3

4 The degn of neted control loop carred out from the nde to the outde of the control tructure. Th, the nner control loop degned frt and then, the outer control loop degned. So, n th cae, the current control loop mut be degned frt. The degn of the current control loop The frt tep to deelop a bac dynamc modellng of the nner current loop. Let conder n, a the output oltage of the IGBT brdge, when the nerter wtchng output oltage aeraged at wtchng frequency. Thu wtchng rpple neglected. If unpolar PWM modulaton condered, n gen by (). DC n mod V () tr p Where: V trp the ampltude of the trangular carrer gnal and mod the modulatng gnal. Then, the aerage nductor oltage (wtchng rpple neglected) gen by (2). dl L L RL L n O dt Snce th already a lnear ytem, the nductor current, can be expreed a follow: L DC mod Vtr p L RL O V DC tr p mod Z ( ) O L (3) At th pont, the power tage already modelled. Therefore, the next tep the modellng of the current ene and condtonng n the Laplace doman. The ened current wll be the frt harmonc component of the actual current (low pa flter) caled down by the enor contant ( ), a expreed n (4). L med co L G c ( ) L Where: the enor contant and co the cutoff angular frequency ( co =2 f co ). From the equaton (3) and (4), the block dagram of the nner control loop can be obtaned and t hown n Fgure 2. Note that the power plant preent two external perturbaton: the nerter nput oltage ( DC ) and the output oltage ( o ) that mut be taken nto account. (2) (4) DC O PLANT L ref L med R() con V DC tr p n L L R L L co Fgure 2: Block dagram of the nner current control loop 4

5 Therefore, the ue of feedforward technque wll help to mplfy the plant that gong to be controlled. The man target of the feedforward the decouplng of the power tage plant from the external perturbaton ( DC and o ). To do o, the nerton of an addtonal tranfer functon that account for the feedforward acton needed: FF() n Fgure 3. Th functon unknown a pror, and t determned a follow. How the feedforward functon (FF()) determned? Snce the objecte of the feedforward the decouplng of the power tage plant from DC and o, then t can be ad that the nerton of FF() ntended to tranform the block dagram n Fgure 2 nto the one depcted n Fgure 3. In each cae, the equaton that defne the nductor oltage ( L ) a a functon of the regulator output (X ) are gen n (5) and (6). DC O L ref R() X X 2 FF() con V DC tr p n L L R L L L med co X FF ( ) Fgure 3: Block dagram of the nner current control loop wth FF X 2 DC DC o L o L V V trp trp (5) L ref X R() L L RL L med L Fgure 4: Objecte block dagram of the nner current control loop wth FF X L (6) Gen (5) and (6), n order to achee a ucceful feedforward, they mut be equal (7). And, from th equalty, the relatonhp between X and X2 can be determned (8) and thu the content of the blackbox FF(). X X DC 2 Vtrp o co Vtrp X 2 ( X o ) DC (8) Therefore, the fnal block dagram of the nner current loop ncludng the feedforward depcted n Fgure 5. (7) 5

6 FF() O DC DC O L ref L med R() V tr p DC n V DC tr p L L R L L co Fgure 5: Block dagram of the nner current control loop wth feedforward of o and DC A a conequence, for the purpoe of the nner current loop compenator, the block dagram reduced to the one hown n Fgure 6. In Fgure 6, t clear that the plant tranfer functon for the purpoe of the current control loop compenator degn reduced to the nductor admttance and t ndependent of the nerter nput oltage ( DC ) and the output oltage ( o ), ee Fgure 5. L ref R() L R L L L med Fgure 6: Block dagram of the current control loop wth FF for the purpoe of the compenator degn So, let degn the current control loop compenator. Degn of the current control loop compenator Snce the condered topology not ncluded wthn the predefned one n SmartCtrl then, the cutom defnton of the ytem needed. Fgure 7: Open Equaton Edtor under Tool Menu co Before tartng the degn proce, the uer can open the text code of the oltage ource nerter and hae a look at the typcal tructure (t not mandatory) and yntax of a text fle that contan the model for plant, enor, loop gan, etc. To do o, pleae go to the Tool Menu and clck on Equaton Edtor. Then clck on open button and browe the fle Sngle Phae VSC.tromod. See Fg. 7. Note that, although any text edtor can be ued to deelop the text contaned n the text code, the extenon.tromod mut be ued n order to guarantee that SmartCtrl recognze the text fle a a model fle. 6

7 When the dered fle elected, the wndow hown on Fgure 8 open. Then pre on equaton edtor, and the text code on ANNEX A can be edted. Input data Wrte a mple to conder the Laplace complex arable n your model. Fgure 8: Equaton Edtor Edton enronment Once the uer famlarzed wth the text code tructure and yntax, the degn proce can tart. Remember that the teadytate alue, plant and enor tranfer functon for both loop can be tored n the ame text code, and the uer only ha to end to the degn enronment the tranfer functon he need for the degn of each partcular loop. Gong back to the degn of the current control loop, the degn a generc control ytem opton gong to be ued (ee Fgure 9). Wthn th opton, an equaton edtor the tool proded for the defnton of both the plant and the enor. Startng wth the plant defnton, the procedure ummarzed n Fgure 0. After clckng on comple, the tranfer functon tored a the plant of the generc control ytem. 7

8 . Defnton of the current loop plant L ref R() L R L L L med co 2. Defnton of the functon to be returned from the one n the fle 3. Comple Fgure 9: Select the Degn a generc control ytem opton Fgure 0: Defnton of the current control loop plant Afterward, the enor tranfer functon mut be defned analogouly to the plant. The proce alo ummarzed n Fgure. After completng the enor defnton, clck O and SmartCtrl wll how the wndow n Fgure 2 to contnue wth the control ytem defnton.. Defnton of the current loop plant L ref R() L R L L L med co 2. Defnton of the functon to be returned from the one n the fle 3. Comple Fgure : Defnton of the current enor Once the plant and the current enor are defned, then the compenator type mut be elected. In th cae, t a PI compenator a hown n Fgure 2. Then the program able to how the oluton map that prode the et of phae margncrooer frequency that led to table oluton. Th oluton map prode an eay tool for the electon of the control loop ntal oluton, for ntance fc=khz and PM=60º (ee Fgure 2), that can be optmzed later. 8

9 Fgure 2: Compenator electon and oluton map (fc=2khz, PM=45º) Clck O to proceed, and the graphc and text panel wll how the Bode plot, Nyqut plot and tranent repone, a well a the oluton map, n order to help the optmzaton of the control loop degn. An optmzed compenator eek to fulfl the followng gudelne: Try to obtan the maxmum open loop gan at any frequency. T() mut perform the hghet alue alway. In that way, the effect of the perturbaton to the control ytem wll be mnmzed. The maxmum crooer frequency (fc) lmted by the effecte cutoff frequency of the current loop. Dynamcal nteracton can occur f outer loop fater than nner loop. It preferable to et below fc. In th way, the current loop a contant wthn the bandwdth of the VSC loop An oerdamped repone n general preferable. Dampng factor ncreang a PM ncreae. Howeer, f a ery hgh PM elected, t would penalze the oerall gan of T() The optmzaton of the compenator performance can be ealy carred out wth the help of SmartCtrl, nce the tranent repone and the Bode and Nyqut plot can be checked multaneouly at a glance. Addtonally, on the rght hand de of the wndow, lder for the crooer frequency and the phae margn are aalable, a well a the oluton map. Th lat one prode the degner wth a powerful tool, nce t how the feable oluton pace for a gen plant and compenator type n a graphcal and traghtforward way. In Fgure 3 t can be een that the ntal oluton (fc=khz, PM=60º) can be mproed and better feature can be obtaned. For ntance, for fc=2khz and PM=45º, a hgher control to output gan acheed. 9

10 fc=khz, PM=60º fc=2khz, PM=45º Fgure 3: Graphc panel from Smartctrl For each degn, checkng the output data panel, the degner wll fnd the reultng compenator gen n dfferent format a depcted n Fgure 4.. p and nt 2. Component alue for analog mplementaton 3. Pole and zero frequency 4. doman coeffcent Fgure 4: Output data panel for the current control loop Regardng the dgtal mplementaton, t alo aalable n SmartCtrl. A ummarzed n Fgure 5, through the dgtal control opton and after defnng the amplng frequency, bt number and accumulated delay, the effect of the dgtal mplementaton can be repreented along wth the analog Bode plot. Addtonally, the compenator Zdoman coeffcent can be found n the output data panel. 0

11 3 Show dgtal control to output tranfer functon T() dgtal (db) T() analog (db) 2 4 T() analog (º) T() dgtal (º) Fgure 5: How to repreent the dgtal mplementaton effect and obtan the dgtal compenator coeffcent. Rght now, the current control loop already degned. So, t tme to begn wth the degn of the oltage control loop. 2 The degn of the oltage control loop Snce the control tructure formed by two neted control loop, the outer oltage loop prode the reference to the nner current loop, whch behae a a controlled current ource a depcted n fgure 6. L O C G C Load O O Voltage enor O med O ref V O ref p I L ref R V n t Fgure 6: Voltage control loop and current control loop beaor Therefore, the output oltage o correpond to equaton (9).

12 o L o RC C (9) Where L gen by (0) and the cloed loop tranfer functon of the current control loop (G) expreed n (). L G ( ) L_ ref R Z L( ) G ( ) R Gc( ) Z ( ) L Where R the current regulator that wa calculated preouly. Fnally, the oltage enor behaor analogou to the one of the current enor, and gen n (2) o med o G ( ) co o So, the block dagram of the oltage control loop the one hown n Fgure. (0) () (2) O PLANT V o ref o med R() G () L C O RC C Fgure : Voltage control loop A n the cae of the current control loop, t would be ueful f the plant could be reduced to the output capactor mpedance. Th, by mean of a feedforward technque, achee a plant ndependent of the current control loop (G()) and the load current ( o ). Followng an analogou procedure to the one explaned for the current control loop, the block dagram of the oltage control loop when a FF mplemented would be the one n Fgure 8. co O FEED FORWARD O PLANT V o ref L C O R() /G G () () R C C o med co Fgure 8: Voltage control loop wth feedforward of the load current and the cloed loop tranfer functon of the current control loop. 2

13 Howeer, whle addng o eay, the mplementaton of /G() n the FF path dffcult, nce t a complex tranfer functon. That beng ad, f the crooer frequency of the oltage control loop low enough, then the cloed loop tranfer functon can be approxmated a a contant (3). And o, the mplementaton of G() now ery eay. G ( ) Where: the current enor contant. Thu, n order to be able to mplement the feedforward, a new degn contrant mut be kept n mnd: the elected crooer frequency of the oltage control loop mut be low enough o that the cloed loop current control tranfer functon behae a a contant. The way n whch th degn contrant taken nto account wll be explaned later. How to obtan and export G() Pror to the degn of the oltage control loop, the cloed loop frequency repone of the current control loop mut be obtaned and exported. In order to be ued later to account for the oltage loop crooer lmtaton that allow the mplementaton of the feedforward. A ummarzed n Fgure 9, to obtan the cloed loop tranfer functon the frt tep to type the obtaned PI contant n order to calculate the cloed loop frequency repone. Next, t needed de defnton of whch functon mut be returned, and fnally clck on comple to calculate the elected functon. A t can be een n Fgure 9, on the rght hand de of the wndow the Bode plot for the condered tranfer functon are hown. (). Type the PI contant calculated for the current control loop 2. Defnton of the functon to be returned from the one n the fle 3. Comple Fgure 9: Summary on how to obtan the current cloed loop tranfer functon Rght afterward the frequency repone can be exported for t later ue, a depcted n Fgure

14 2 3 Fgure 20: Summary on how to export a tranfer functon after complng t Degn of the oltage control loop compenator Aumng that the feedforward mplemented, then for the purpoe of the oltage loop compenator, the block dagram reduced to the one hown n Fgure 2. A t can be een, the plant reduced to the output capactor mpedance, and t ndependent from the cloed current loop and from the load current. V o ref R() R C C O o med Fgure 2: Block dagram of the oltage control loop wth FF for the purpoe of the compenator degn So, the frt tep the defnton of the plant, a ummarzed n Fgure 22, and the defnton of the enor n Fgure 23. co 4

15 . Defnton of the oltage loop plant. Defnton of the oltage loop enor V o ref o med R() C R C O V o ref o med R() C R C O co co 2. Defnton of the functon to be returned from the one n the fle 3. Comple 2. Defnton of the functon to be returned from the one n the fle 3. Comple Fgure 22: Defnton of the oltage loop plant Fgure 23: Defnton of the oltage loop enor And fnally, elect the compenator type and ue the oluton map to tablh the crooer frequency and the phae margn (ee Fgure 24) Fgure 24: Selecton of the compenator type, the crooer frequency and the phae margn for the oltage control loop Be aware that, n th cae, the modulator mut be et to hae unty gan, nce there no modulator n the outer control loop. Once the ytem defned, the reult panel are dplayed and the regulator can be calculated. It hould be remnded that there an addtonal degn contrant regardng the maxmum crooer frequency n order to guarantee that the feedforward work. In order to keep th retrcton n mnd whle degnng the oltage control loop PI, t recommended to nclude the frequency repone of the current cloed loop n the Bode plot. Th frequency repone wa preouly exported, and now t gong to be mported to be repreented together wth the Bode Plot of the oltage control loop. The proce ummarzed n Fgure 25. Followng the ame export/mport proce, the control to output frequency repone of the current control loop alo ncluded for addtonal nformaton durng the oltage control loop degn. 5

16 3 8 2 Modulu and phae of G () 4 Select the fle Fgure 25: Import the current cloed loop frequency repone The mported cloed loop frequency repone prode nformaton related to the behaor of G() (n order to predct the FF performance) and the control to output of the current control loop etablhe the maxmum crooer frequency of the oltage control loop to aod dynamc nteracton between the two neted loop. (ee Fgure 26) G() current cloed loop tranfer functon Gcl() plant of the oltage control loop wth FF T() Control to output tranfer functon from the current loop T() Control to output tranfer functon Fgure 26: Bode plot for the degn of the oltage control loop compenator A tated before, the outer loop mut be lower than the nner one, n order to aod dynamc nteracton between the loop and thu ntablty. Th o, becaue the plant of the nner loop can 6

17 be aumed to be almot contant wthn the bandwdth of the oltage control loop. Therefore, n th tuaton the aumpton made whle degnng the feedforward alo ald (G ()/) and t wll be able to elmnate the nfluence of the current cloed loop. So, t can be ad that the maxmum crooer frequency for the oltage control loop lmted by the crooer frequency of the current control loop. In order to llutrate th effect, let conder the chematc hown n Fgure 20 and the mulaton reult proded n Fgure 28, Fgure 29 and Fgure 30. In Fgure 28 t can be obered that the output oltage follow the reference wthout any error and t able to attend to ether nput oltage or load current tep almot ntantly, een though the crooer frequency of the oltage control loop only 500 Hz. In Fgure 29, t hown that een wth a oltage loop crooer frequency equal to the one n the current loop, the ytem performance tll table. Howeer, when a hgher crooer frequency elected, t hown n Fgure 30 that both loop nteract and tend to the ntablty. Fgure 27: Smulaton chematc wth nput oltage tep and load current tep carrer Mod_ Mod_2 Vdc Io Vo_ref Fgure 28: Smulaton reult wth FF and a oltage control loop characterzed by fc=500hz and PM=30º 7

18 carrer Mod_ Mod_2 Vdc Io Vo_ref Fgure 29: Smulaton reult wth FF and a oltage control loop characterzed by fc=2000hz and PM=30º carrer Mod_ Mod_2 Vdc Io Vo_ref Fgure 30: Smulaton reult wth FF and a oltage control loop characterzed by fc=2300hz and PM=30º At th pont, the procedure to degn the current and the oltage control loop of a ngle phae oltage ource nerter wth SmartCtrl ha been completed. It notceable that, gen the model equaton (plant and enor) of any ytem, SmarCtrl prode a ery fat and effcent tool to accurately degn any control loop. 8

19 ANNEX A: Text code to degn the doubleloop control of a nglephae oltageource nerter //****************************************************** // ** SnglePhae Voltage ource Inerter ** // ** ** // ** A. Lazaro ** // ***************************************************** // ** INPUT DATA ** // // Inerter Sn = 5e3 // Nomnal apparent power Vo = 230 // Output Voltage (rm) f = 50 // Frequency of the output oltage // PWM modulator fw = 0e3 // wtchng frequency Vp = 2 // carrer gnal peak alue Vpp = 2*Vp //carrer gnal peak to peak alue Gmod = /Vpp // modulator gan // Output LC flter L = 200e6 //Flter nductance RL = 00e3 // Inductance ESR C = 33e6 RC = 0e3 // Current enor = 0.25 // gan fco = 3e3 // cutoff frequency wco = 2*PI*fco Gc = /(/wco) // Voltage enor = 0.02 // gan fco = 3e3 // cutoff frequency wco = 2*PI*fco G = /(/wco) // ** INNER CURRENT LOOP ** // ZL = L*RL Gc = /ZL p = Tc = e6 R = p*(*tc)/(*tc) //Compenator tranfer functon T = (/ZL)*R*Gc*Gmod //Control to output tranfer functon of the current loop G = (/ZL)*R*Gmod /(T) //Cloedloop gan of the current loop // ** OUTER VOLTAGE LOOP ** // ZC = (/C*)RC Gcl = G*ZC // Voltage loop plant wthout o feedforward Gcl2 = ZC // Voltage loop plant wth o feedforward return Gcl2 9