Progre I Electromagetic Reearch C, Vol. 9, 29 224, 29 Virtual Sychroou Motor Dyamic Power Decouplig Strategy Xitia Liu, Yucai Li *, Yao He, Xixi heg, ad Guojia eg Abtract Due to the exitece of power couplig the virtual ychroou motor (VSG) will lead to overhoot fluctuatio i the power adjutmet proce, thu affectig the cotrol performace. Compared to the traditioal direct curret cotrol iverter baed o coordiate traformatio, VSG model i more complex ad difficult to achieve decouplig. Thi paper preet a dyamic power decouplig method by tudyig the couplig relatiohip betwee active power ad reactive power of VSG. Firtly, the iverter grid-coected model i etablihed, ad the power expreio i aalyzed whe the iverter output impedace i egligible. The the virtual active power ad reactive power expreio are obtaied through coordiate traformatio. Several key tate equatio ad virtual tate of the VSG are obtaied. The power expreio perform mall igal perturbatio to obtai the dyamic model of the VSG. From thi, the dyamic model of the VSG ca be aalyzed to obtai the couplig relatiohip betwee the dyamic power, ad the erie power compeatio i ued to decouple the dyamic power couplig. Fially, the correcte of the theoretical aalyi ad the effectivee of the decouplig method are verified by imulatio ad experimet.. INTRODUCTION Nowaday, eergy crii ad evirometal problem are becomig more ad more eriou. Ditributed geeratio techology i a effective mea to olve thi problem []. I traditioal power ytem, power grid coectio i realized by ychroou machie [2]. With more ad more ditributed eergy itegrated ito the power grid [3], the tructure of a traditioal power ytem i affected o that the ditributed eergy eed to achieve power regulatio [4], ad the cocept of virtual ychroou geerator (VSG) i propoed [5]. VSG fully imulate the characteritic of ychroou motor ad i expected to be a effective way to olve the ecurity problem caued by large amout of ditributed eergy itercoectio. Sice it cocept wa put forward, it ha attracted much attetio [6 ]. The reearch o VSG i maily focued o the improvemet of iverter cotrol performace. Referece [9] poit out that the phae-locked loop ca be omitted i the cotrol ytem becaue of the ychroizatio characteritic of virtual ychroou motor, o that the whole cotrol ytem tructure i implified, ad the ytem performace i greatly improved. Referece [] how that active ad reactive loop are approximately decoupled after mall igal modelig, o the parameter of active ad reactive loop ca be deiged eparately, which greatly implifie the parameter deig. Referece [] propoe a method of addig dampig correctio loop i VSG algorithm, which add a parameter to the dampig coefficiet. By adjutig thi parameter, the repoe peed of power regulatio ca be improved. However, thee method do ot coider the couplig betwee active power ad reactive power. I [9], the couplig betwee active ad reactive power i ot coidered, reultig i couplig power fluctuatio ad teady-tate error i power regulatio. The parameter deig method i propoed i [] whe the iductace i much larger tha the reitace, i.e., X R. The author aalyze that the Received 25 October 28, Accepted 26 December 28, Scheduled 5 March 29 * Correpodig author: Yucai Li (yucai.li26@foxmail.com). The author are with the Hefei Uiverity of Techology, Hefei, Chia.
2 Liu et al. active power ad reactive power are approximately decoupled whe the iductace i much larger tha the reitace X R, but the power i ot completely decoupled at thi time. The author oly make a approximate aalyi, o the power couplig i till dyamic. State characteritic are ifluetial. The optimizatio method of virtual ychroou motor cotrol propoed i [] i alo baed o the coditio that the iductace i much larger tha the reitace X R. Itipoitedoutthatthe couplig effect of power regulatio after addig dampig correctio loop i weakeed properly, but the reao are ot aalyzed i depth. Aimig at the decouplig problem, mot of the curret-cotrolled iverter baed o coordiate traformatio are tudied. Referece [2] aim at the couplig betwee the dq axe of LCL filter gridcoected iverter. The compoet of other axe iformatio are ijected ito each axi cotroller, ad the compoet ijected are equal to the couplig magitude produced by the cotrolled object, but the directio i revered, o that decouplig ca be realized. Referece [3] alo tudie the dyamic couplig betwee the dq axe of the LCL grid-coected iverter. Three-loop feedback compeatio method i ued to effectively uppre the couplig overhoot i the proce of dyamic power regulatio. However, for VSG, it model i o complex that the decouplig i difficult to achieve. At preet, mot of the decouplig reearch o VSG i tatic couplig [4 6]. There are few tudie o dyamic couplig. Referece [7] aalyze the dyamic couplig betwee active power P ad reactive power Q accordig to the itataeou power theory. However, due to the complexity of the model ued, the couplig relatiohip i alo complicated, ad the mai reao of affectig the dyamic couplig i ot poited out, o thi model i ot uitable for decouplig reearch. I view of the above problem, the VSG dyamic couplig model etablihed i thi paper ha a clear tructure, which ca effectively olve the problem that the VSG couplig model i complex ad difficult to aalyze the couplig caue, ad ha the advatage of eay decouplig. Firtly, the baic priciple of VSG i aalyzed, ad the the tatic couplig relatiohip betwee active power ad reactive power of virtual ychroou motor i aalyzed accordig to the circuit theory. The expreio of virtual active power ad reactive power i obtaied by coordiate traformatio. O thi bai, the dyamic couplig of the ytem i modeled ad aalyzed by mall igal aalyi method, ad the decouplig i the dyamic regulatio proce i realized by erie compeatio method. Fially, the theoretical aalyi i verified by imulatio ad experimet. 2. COUPLING CHARACTERISTICS OF VSG 2.. VSG Power Loop ad It Cotrol Strategy VSG DC-ide voltage V i i defied. Iverter are coverted ito three-phae alteratig curret by a three-phae bridge arm ad a LC filter. u abc ad i abc are output voltage ad curret of iverter. The output active power P ad reactive power Q of the iverter ca be calculated by the itataeou power theory [8] after the traformatio of u abc ad i abc by Park. The expreio i P = 3 2 (u di d u q i q ) Q = 3 () 2 (u qi d u d i q ) I the formula, u d ad u q are the active ad reactive compoet of u abc i a dq coordiate ytem after Park traformatio. i d ad i q are the active ad reactive compoet of i abc. The whole cotrol ytem coit of ier loop ad outer loop. The outer loop i VSG algorithm a how i Figure [5]. The ier loop i PR cotroller. VSG algorithm maily iclude active power cotrol loop ad reactive power cotrol loop. Active power loop maily realize active-frequecy cotrol, imulate the rotor motio equatio of ychroou motor, realize primary frequecy modulatio ad iertia regulatio, while reactive power-voltage cotrol loop maily imulate the excitatio equatio of the ychroou motor ad realize the primary voltage regulatio characteritic of the ychroou motor. Accordig to Figure, the mai equatio of VSG ca be obtaied a how below J dω dt = T et T D p (ω ω ) (2)
Progre I Electromagetic Reearch C, Vol. 9, 29 2 D ω p T et P Q et ω Q J K ω M f i f θ Formula (6) e D q V o V Figure. VSG algorithm. θ = ωdt (3) T = P ω (4) K dm f i f = Q et Q D q (V V o ) (5) dt I the formula, J i the momet of iertia, D p the dampig coefficiet, ω themehideychroou agular velocity, ω the referece agular velocity, T et the mechaical torque, T the electromagetic torque, K the itegral coefficiet, Q et the et value of reactive power, Q the output reactive power of iverter, D q the droop coefficiet of reactive loop, V the rated voltage amplitude, ad V o the output voltage amplitude of iverter. Accordig to the active power loop, the phae agle θ ad agular velocity ω ca be calculated, ad the voltage iformatio M f i f ca be calculated by the reactive power loop. The electromotive force referece value e tramitted to the ier loop of the VSG loop ca be calculated a how i Equatio (6). e a = M f i f ω i θ ( e b = M f i f ω i θ 2π ) 3 (6) ( e c =M f i f ω i θ 4π ) 3 I order to improve the trackig accuracy [9], the ier loop adopt the PR cotroller, ad the filtered iductor curret igal i ued a the cotrol amout. Accordig to the LC filter circuit tructure, the followig formula ca be obtaied. e u o = L di ir (7) dt where e i the iverter termial voltage, u o the iverter output voltage, L the filter iductor, R the paraitic reitace, ad i the iductor curret. Calculate the referece value i of the iductor curret i l accordig to Equatio (7), ad the obtai the error igal by collectig the iductor curret i the circuit. The error igal i et to the ier loop PR cotroller, ad the PR cotroller ca perform o-differece cotrol o the AC igal. G PR () =K P 2K r 2 ωo 2 (8)
22 Liu et al. Figure 2. The truct graphic of whole ytem. where K p i the proportioal coefficiet, K r the reoace coefficiet, ad ω the reoat frequecy. The error igal i paed through the PR cotroller to obtai the SVPWM igal for drivig the IGBT, ad the whole cotrol ytem tructure i how i Figure 2. 2.2. Couplig Aalyi I order to aalyze the dyamic couplig characteritic of the VSG, the firt tep mut be to obtai a dyamic couplig model of the VSG. Figure 3 how the power flow graph of the iverter grid-coected circuit coiderig the iverter output impedace ad grid-coected lie impedace. I Figure 3, o i the iverter ytem output impedace, the grid-coected lie impedace, E the iverter output voltage, ad it phae agle i δ. U i the grid ide voltage, ad it phae agle i. o θ E δ U Figure 3. The graphic of power flow. Accordig to the tructure diagram how i Figure 2, the expreio of o ca be obtaied. Let the trafer fuctio of K SVPWM i Figure 2 be G SVPWM (), ad the gai expreio ca be expreed by the followig formula [2]. G SVPWM () = (.5T ) 2 2 6(.5T ) 2 (.5T ) 2 2 (9) 6(.5T ) 2 where T i the witchig period of SVPWM, o o ca be obtaied from the Mao gai formula. o = u o i o = (L R)L (LC 2 )(L R)G PR ()G SV PWM ()(LC 2 CR ) Accordig to the relevat parameter of Table, the Bode diagram of o ca be obtaied a how i Figure 4. It ca be ee from Figure 4 that the amplitude of the ytem impedace i very mall at the power frequecy of 5 Hz, o whe calculatig the impedace of the grid coectio lie ca igore the output impedace of the ytem. At thi time, the impedace of the grid i the power flow diagram how i Figure 3 i oly, adthereare θ = R jx, wherer ad X are the grid-coected lie reitace ad iductive reactace, o the power ijected ito the grid ca be expreed below. () E P = R 2 [R(E U co δ)xu i δ] X2 () E Q = R 2 X 2 [RU i δ X(E U co δ)]
Progre I Electromagetic Reearch C, Vol. 9, 29 23 5 Bode Diagram Magitude (db) -5 - -5 9 Phae (deg) -9-8 -27 2 Frequecy (Hz) Figure 4. The bode graphic of ytem impedace. Table. Three-phae VSG parameter. Parameter value Iput voltage U i /V 7 Grid voltage U g /V 22 Output power P o /kw Power frequecy f/hz 5 P-F droop coefficiet D p 8 Dampig coefficiet J. Reactive loop coefficiet K Reoace coefficiet K r 3 Filter Iductor L /mh.285 Paraitic reitace R /Ω.3 Filter capacitor C/uF 5 Grid-coected iductor L 2 /mh.285 Grid-coected reitor R/Ω.3 Q-U droopig coefficiet D q 32 Proportio factor K p.5 Steady tate power agle δ.5 If the mall igal i directly made at thi time, the obtaied dyamic couplig model will be too complicated, which make decouplig difficult to implemet. Therefore, the coordiate traformatio ca be doe firt to obtai the virtual work expreio, ad the traformatio method i a follow [2] { P = P i θ Q co θ Q (2) = P co θ Q i θ where θ i the impedace agle of the grid-coected lie, ad co θ = R/, iθ = X/ [22].
24 Liu et al. Equatio (3) ca be obtaied by Equatio () ad (2) P EU i δ = (3) Q E(E U co δ) = I the formula, δ i the power tramiio agle of the grid coectio, which ca be obtaied by the followig formula δ = ω ω g dt (4) I the formula, ω i the iverter output voltage agular frequecy, ad ω g i the grid ide voltage agular frequecy. Figure 5. The mai circuit graphic with virtual power. Figure 5 how the tructure of the mai circuit after the coordiate traformatio i added. At thi time, the power fed back to the VSG algorithm i the virtual active ad reactive power, o the power value i Equatio (2) ad (5) alo become virtual power, a follow J dω dt = P et ω P ω D p(ω ω ) (5) K dm f i f dt = Q et Q D q (V V o ) (6) At thi poit, the mall-igal aalyi ca be ued to obtai the dyamic couplig model of the ytem. Perform mall igal diturbace o the variable E, δ, P, Q, P et, Q et, ω, M f i f i Equatio (6), (3) (6), the elimiate the DC amout o both ide of the equatio, igore the diturbace amout of more tha two time [23], ad coider the approximate relatiohip co ˆδ, i ˆδ ˆδ to obtai the followig equatio, where δ i the power agle at teady tate. ˆP et D p ˆω ˆP = J dˆω ω ω dt (7) ˆQ et D q Ê ˆQ = K d M ˆ f i f dt (8)
Progre I Electromagetic Reearch C, Vol. 9, 29 25 ˆδ = ˆωdt (9) Ê ω Mˆ f i f ωˆ (2) ˆP = 3UE co δ ˆδ 3U i δ Ê (2) ˆQ = 3(2E U co δ ) Ê 3EU i δ ˆδ (22) The Laplace traform of Equatio (7) (9) yield the followig equatio ˆP et ˆP =(J D p )ˆω (23) ω ω ˆQ et ˆQ =(K D q ) Mˆ f i f (24) ˆδ = ˆω (25) Accordig to Eq. (2) (25), the dyamic couplig model tructure diagram ca be obtaied a how i Figure 6. The couplig relatiohip betwee the active power loop ad reactive power loop ca be ee, ad the couplig amout i related to the voltage amplitude E, teady tate power agle δ, ad grid-coected impedace. P 'et ' et Q ω ( J D ) ω K D q p 3UE coδ 3UE iδ 3U iδ 3(2E Uco δ) P ' Q ' Figure 6. The dyamical couplig model. 3. DECOUPLING STRATEGY For the couplig tructure diagram how i Figure 6, erie compeatio ca be itroduced to decouple the dyamic couplig. The ytem how i Figure 7 i a ytem with a implified tructure of the dyamic couplig model of Figure 6 ad itroduced ito the erie compeatio ytem. The ytem i a two-iput ad two-output ytem. If the cloed loop of the ytem ca be decoupled, the ope-loop trafer fuctio i a diagoal array [24], i.e., the output of the iput X () toy 2 () i the dotted lie frame i, ad the output of the iput X 2 () toy () i alo. From the figure, it ca be cocluded that the iput X () toy 2 () output i zero ad eed to meet the followig formula. G c2 ()G 2 ()G 2 ()G 2 () = (26) Ca be olved G c2 () =[G 2 ()G 2 ()]/G 2 () (27)
26 Liu et al. erie compeatio U () G () c X () G() G2() Y() G () c2 G () G () 2 2 U () 2 G X () 2 G () 2 c2 () G () c2 G () 2 Y () 2 Figure 7. The truct graphic with erie compeatio. For the ame reao, the output of iput X 2 () toy () i zero, ad the followig formula eed to be atified. G c2 ()[G ()G 2 ()] G 2 () = (28) Equatio (29) ca be derived from Equatio (28). G c2 () =G 2 ()/[G ()G 2 ()] (29) Therefore, the tructure diagram how i Figure 6 ca be olved accordig to erie compeatio. G c2 () = 3UEi δ 3(2E U co δ ) (3) VSG geerally ha E U i power regulatio, o Equatio (3) ca be implified to G c2 () E i δ (2 co δ ) (3) where E i the maximum value of the iverter output voltage of 3 V, ad δ i the power agle at teady tate, which ca be obtaied by itegratig the differece betwee the iverter output voltage agular frequecy ad the grid voltage agular frequecy. P 'et ' et Q ω ( J Dp) 3UEcoδ 3Uiδ Ei δ 3UEiδ 3(2E U coδ ) (2coδ ) i δ 3U iδ Eco δ iδ ω K D q 3(2EU coδ ) P ' Q ' Figure 8. The dyamical model with erie compeatio added.
Progre I Electromagetic Reearch C, Vol. 9, 29 27 Equatio (32) ca be derived for the ame reao G c2 () = 3U i δ 3UEco δ 3U i δ From U E, Equatio (32) ca be implified to i δ G c2 () (33) E co δ co δ Equatio (3) ad (33) are the compeatio amout of the dyamic decouplig decribed i thi paper. Figure 8 how the ytem tructure diagram after addig the erie compeatio to the VSG dyamic model. 4. SYSTEM STABILITY ANALYSIS 4.. Active Loop Stability The mall-igal model how i Figure 6 ca be viewed a a two-iput two-output ytem. Whe aalyzig the performace of the active loop, the reactive power igal ca be regarded a a diturbace igal ad et to zero [25], o the mall-igal model how i Figure 6 ca be implified to Figure 9. Accordig to Figure 9, the active power cloed-loop trafer fuctio ca be obtaied. Amog them a =3UK i δ G() rpl = (32) a 2 b c d 3 e 2 f g (34) b =3UD q i δ 3UEK co δ 9Uω (2E U co δ )iδ c =3UEco δ D q 9UEco δ ω (2E U co δ ) 9U 2 E i 2 δ ω d = 2 Kω J e = 2 Kω D p ω J 2 D q 3(2E U co δ )ω 2J 3U i δ K f = ω D p 2 D q 3ω 2D p(2e U co δ )3U i δ D q 3UEK co δ 9U i δ ω (2E U co δ ) g =3UEco δ D q 9UEco δ ω (2E U co δ ) 9U 2 E i 2 δ ω (35) ω ( J D ) P 'et p ω 3UE coδ P ' 3UE iδ 3U iδ ω K D q 3(2E U coδ ) Figure 9. The implified chematic of active power loop.
28 Liu et al. P 'et ω ( J D ) p δ 3UE coδ 3U iδ P ' Figure. The chematic of decouplig active power loop. Whe the erie compeatio decouplig i added, the active power loop graph ca be obtaied a how i Figure, ad the cloed loop trafer fuctio of the active loop i 3UEco δ 3U i δ G() dapl = ω J 2 (36) (ω D p 3U i δ ) 3UEco δ It ca be foud that the cloed loop pole of the active loop at thi time i adpl = (ω D p 3U i δ ) ± (ω D p 3U i δ ) 2 2ω JUEco δ (37) 2ω J 4ac =2ω JUE co δ (38) I formula (38), δ doe ot exceed 9 degree [] whe it i coected to the grid, o that Equatio (38) greater tha zero i cotat, i.e., the cloed loop pole of the active loop after decouplig i alway located i the left half axi after erie compeatio, ad the active loop remai table for ay parameter chage. The root trajectory chage whe the impedace traform i ot decoupled ad decoupled are how i Figure (a) ad (b). A how, the pole of the udecoupled tate ad decoupled tate are ditributed o the left ide of the axi, i.e., the tability of the active loop after erie compeatio doe ot chage. Imagiary Axi (ecod - ) 4 3 2 - -2 4.54.7.9.9 Pole-ero Map 6e3.4.3.2.3.6 5e3 4e3 3e3 2e3 e3 e3 2e3 3e3 4e3-3.7 5e3.54.4.3.2.3.6-4 6e3-3 -2.5-2 -.5 - -.5 Real Axi (ecod - ) 4 (a) Imagiary Axi (ecod - ) 5 4 3 2.985.4e3.2e3 e3 8 6 4 2 -.985-2 -3.94 Root Locu.86.76.64.5.34.6.94-4.86.76.64.5.34.6-5 -9-8 -7-6 -5-4 -3-2 - Real Axi (ecod - ) (b) Figure. Active power loop root locu. (a) The root locu i udecoupled mode with chaged. (b) The root locu plot i decoupled mode with chaged. 4.2. Reactive Loop Stability Similarly, for the two-iput ad two-output ytem how i Figure 6, whe aalyzig the reactive udecoupled loop, the active power referece ca be regarded a a diturbace ad et to zero. At thi time, the reactive loop i implified a how i Figure 2.
Progre I Electromagetic Reearch C, Vol. 9, 29 29 ' et Q ω K D q 3(2E Ucoδ ) Q ' 3U iδ 3UE iδ ω ( J D ) p 3UE coδ Figure 2. The implified chematic of reactive power loop. ' et ω E 3(2E coδ ) Q Q K D q Figure 3. The chematic of decouplig reactive power loop. U ' Accordig to Figure 2, the reactive power trafer fuctio at thi time ca be obtaied a a 2 2 b 2 c 2 G() rpl = d 2 3 e 2 2 (39) f 2 g 2 Amog them a 2 =3ω 2J(2E U co δ ) b 2 =3ωD 2 p (2E U co δ ) c 2 =9ω UEco δ (2E U co δ ) 9U 2 Eω i 2 δ d 2 = 2 Kω J (4) e 2 =3UK i δ 2 ω JD q 2 Kω D p 3ω 2J(2E U co δ ) f 2 = 2 ω D p D q 3UEK co δ 3U i δ D q 3ω 2D p(2e U co δ ) g 2 =3UEco δ D q 9ω UEco δ (2E U co δ ) 9U 2 Eω i 2 δ The reactive power loop after addig erie compeatio decouplig i how i Figure 3. At thi time, the cloed loop trafer fuctio of the reactive loop i 3ω (2E U co δ ) G() drpl = (4) K D q 3ω (2E U co δ ) The cloed loop pole of the reactive loop i drpl = D q 3ω (2E U co δ ) (42) K It ca be ee from Equatio (42) that the cloed loop pole of the reactive loop at thi time i alway true for ay parameter chage pole le tha, which mea that the reactive loop i table for ay parameter chage. The root trajectory of the reactive power loop udecoupled tate ad the erie compeatio decouplig tate with impedace chaged are how i Figure 4(a) ad 4(b). The compario graph how that addig erie compeatio doe ot chage the ytem tability. Whe there are
22 Liu et al. Pole-ero Map.5.8.998.996 Root Locu.993.986.965.86 Imagiary Axi (ecod - ) 4 2.4e7.2e7-2 -4-6 e7 8e6 6e6 4e6 2e6.5-9 -8-7 -6-5 -4-3 -2 - Real Axi (ecod - ) 7 (a) Imagiary Axi (ecod - ).6.999.4.2.2.75 -.2.5.25..75.5.25 -.4.999 -.6.998.996.993.986.965.86 -.8 -.4 -.2 - -.8 -.6 -.4 -.2.2 Real Axi (ecod - ) (b) Figure 4. Reactive power loop root locu. (a) The root locu plot i udecoupled mode with chaged. (b) The root locu plot i decouplig mode with chaged. three pole i the couplig, oe pair of cojugate pole i ditributed ear the zero axi, ad after the decouplig i added, oly oe pole i ditributed o the left ide of the axi, ad the tability i ehaced. 5. SIMULATION AND EXPERIMENTAL VERIFICATION 5.. Simulatio Aalyi I order to verify the above aalyi reult, the correcte of the imulatio argumetatio aalyi ad the effectivee of the decouplig method are etablihed i MATLAB/Simulik. The parameter are how i Table. Figure 5(a) how the imulatio of the grid-coected lie reitace R =.3 Ω whe the relative iductace i ot egligible. The active power P i et to 5 kw at.2 ad et to W at.5. At thi time, a large couplig overhoot occur i the reactive power, ad a teady tate error occur at teady tate, i which the cotrol i ivalid for the cotrol ytem at thi time. Figure 5(b) how the P[kW/div] P P[kW/div] Q Q[kVar/div] Q Q[kVar/div] P t[m/div] (a) t[m/div] (b) Figure 5. Power regulatio. (a) R =.3 Ω. The active power et to 5 kw the decreae to. (b) R =.3 Ω. The reactive power et to 5 kw the decreae to.
Progre I Electromagetic Reearch C, Vol. 9, 29 22 P' [kw/div] Q' [kw/div] P ' Q ' P 2 ' Q 2 ' P ' P 2 ' Q ' Q 2 ' iabc[5a/div] i abc t[m/div] (a) t[m/div] (b) P' [kw/div] Q' [kw/div] P 2 ' Q ' Q 2 ' P P ' ' P 2 ' P ' P 2 ' Q ' Q 2 ' iabc[5a/div] i abc t[m/div] (c) t[m/div] (d) Figure 6. The power regulatio whe erie compeatio added ad curret plot. (a) R =.3Ω. The compared plot whe active power regulatio. (b) The curret graphic whe active power regulatio. (c) R =.3 Ω. The compared plot whe reactive power regulatio. (d) The curret graphic whe reactive power regulatio. imulatio graph whe the reactive power i et to 5 kvar at.2 ad Var at.5. It ca be ee from the figure that the active power alo ha a large couplig overhoot durig dyamic adjutmet. Figure 6(a) how the imulatio graph whe the active power i et to 5 kw at.2 ad W at.5 after the coordiate traformatio. The active power ad reactive power of the feedback cotrol algorithm are both virtual active ad reactive. It ca be ee from the graph that the virtual reactive power couplig overhoot i effectively uppreed, ad the couplig teady-tate error durig active adjutmet ca alo be elimiated. However, the dyamic couplig at thi time i ot completely elimiated. Q 2 i a imulatio reult graph after icreaig the erie compeatio. It ca be ee that the couplig overhoot i completely uppreed, which prove the correcte of the dyamic couplig aalyi ad the effectivee of the decouplig method, ad Figure 6(b) how the iverter output curret graph at power regulatio at thi time. Figure 6(c) how the imulatio reult whe the reactive power i et to 5 kvar at.2 ad Var at.5. P i the imulatio graph after icreaig the coordiate traformatio. It ca be ee from the figure that the power i active at thi time. The power dyamic couplig overhoot i reduced by early 65%, ad P 2 i the imulatio graph after the erie compeatio decouplig accordig to the aalyi of Sectio 3. It ca be ee that the dyamic couplig overhoot at thi time i alo effectively uppreed. Figure 6(d) how the curret graph whe the power i adjuted. 5.2. Experimetal Aalyi I order to verify the theoretical aalyi ad imulatio reult, a experimetal platform wa built. Figure 7 how the experimetal platform. The mai cotrol DSP ue TMS32F282. The amplig frequecy i 2 khz, ad the witchig frequecy i 2 khz. Figure 9(a) how the voltage ad curret
222 Liu et al. Figure 7. The experimet platform. ia[2a/div] ua[4v/div] u a i a P Q Q[5kVar/div] P[5kW/div] Q[2.5kVar/div] P[2.5kW/div] P' Q' t[m/div] (a) t[/div] (b) Figure 8. Experimetal power regulate graph. (a) The power regulate i udecoupled mode. (b) The power regulate i decouplig mode. ia[2a/div] ua[2v/div] u a i a ia[a/div] ua[v/div] u a i a t[m/div] (a) t[m/div] (b) ia[a/div] ua[v/div] u a i a t[m/div] (c) Figure 9. Experimetal curret graph. (a) The voltage ad curret plot whe ychroize to power grid. (b) The voltage ad curret plot whe oly active power export. (c) The voltage ad curret plot whe both active ad reactive power export.
Progre I Electromagetic Reearch C, Vol. 9, 29 223 waveform durig the grid-coected proce. Figure 8(a) how the power adjutmet patter ad the output voltage ad curret graph whe o decouplig meaure are applied. The active power i et to 5 kw at, ad the reactive power i et to 5 kvar at 2. It ca be ee from the experimetal diagram that the couplig overhoot i large durig the power adjutmet proce whe o decouplig meaure are applied, which eriouly affect the dyamic performace. Figure 8(b) how the power adjutmet waveform after addig decouplig meaure. The active power i et to 2 kw at.5, ad the reactive power i et to 5 kw at 3.5. The reactive power et to 5 kvar at 5, ad the reactive power et to at 6. It ca be ee from the experimetal graph that the couplig overhoot i effectively uppreed, thu verifyig the correcte of the theoretical aalyi. Figure 9(b) how the curret-voltage graph whe oly active power i output. It ca be ee that the phae agle betwee voltage ad curret i. Figure 9(c) how the voltage-curret graph whe oly reactive power i output. At thi time, there i a phae agle differece betwee them. 6. CONCLUSION Ditributed eergy geeratio techology i a effective olutio to today eergy crii ad evirometal problem, but exceive ditributed eergy grid have a great impact o the tructure of the grid. VSG techology i a effective way to olve thi problem. However, due to the couplig betwee power i the VSG power regulatio proce, the dyamic performace of the ytem i affected. Thi paper aalyze the mai factor cauig power couplig ad adopt decouplig meaure. The cocluio are a follow: () Whe the relative iductace of the grid-coected lie i ot egligible, the degree of couplig i greatly icreaed, ad the occurrece of teady-tate error caue the failure of the cotrol. (2) The coordiate traformatio obtaied by grid-coected impedace ca uppre the dyamic couplig overhoot to ome extet, elimiate the couplig caued by the reitor, elimiate the teady-tate error, ad improve the power dyamic adjutmet performace of the feedback back VSG algorithm. (3) The mall-igal aalyi method i ued to obtai the couplig relatiohip betwee the active loop ad reactive loop, o that the etire VSG mall-igal model ca be obtaied. The couplig betwee the loop ca be ee from the etire VSG tructure diagram, ad decouplig ca be achieved by erie compeatio. REFERENCES. Gao, Y. ad Q. Ai, Hierarchical ditributed coordiatio cotrol of active ditributio etwork with pare commuicatio i micro-grid etwork, Automatio of Electric Power Sytem, Vol. 4, 9, 28. 2. Geg, M., Y. Dig, Y. Wag, et al., Micro-et- Orgaic Cell i the future eergy iteret ytem, Automatio of Electric Power Sytem, Vol. 4, No. 9,, 27. 3. Ha,.-X., PowerSytemAalyi, 993. 4. Raj, D. C. ad D. N. Gaokar, Frequecy ad voltage droop cotrol of parallel iverter i microgrid, 26 IEEE 2d Iteratioal Coferece o Cotrol, Itrumetatio, Eergy & Commuicatio (CIEC), 47 4, 26. 5. hog, Q. C. ad G. Wei, Sychroverter: Iverter that mimic ychroou geerator, IEEE Traactio o Idutrial Electroic, Vol. 58, No. 4, 259 267, 2. 6. Nataraja, V. ad G. Wei, Almot global aymptotic tability of a grid-coected ychroou geerator, arxiv preprit arxiv:6.4858, 26. 7. Nataraja, V. ad G. Wei, Sychroverter with better tability due to virtual iductor, virtual capacitor ad ati-widup, IEEE Traactio o Idutrial Electroic, Vol. PP, No. 99,, 27.
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