Evaluation of the Accuracy of Real-time Digital Simulator Voltage Source Converter Models Determined from Frequency Scanning

Transcription

1 valuation of the Accuracy of Real-time Digital Simulator Voltage Source Converter Moel Determine from Freuency Scanning Yi Qi, Aniruha Gole, Hui Ding, Yi Zhang Abtract Two type of moeling metho for the Voltage Source Converter (VSC) are typically ue in a real time igital imulator (rt). One ue the ON an OFF reitance to repreent the ifferent witching tate (calle a the R moel). The other, referre to a the LC moel, i more recent an fater, however make approximation a it moel the ON witch a a mall inuctor an the OFF witch a a mall capacitor in erie with a reitor. Hence, the accuracy of the LC moel i ometime uetione, with the upicion that the L an C element may reult in an unacceptably large error in the freuency repone characteritic. To valiate the accuracy of the LC type moel, the tate pace repreentation of the converter i evelope to get the analytical approximation of freuency impeance. Then a freuency can i conucte on the LC type a well a the R type converter via an rt bae MT imulation to obtain the freuency impeance. The comparion between thee three reult prove that with properly electe parameter for the L an C component, the LC moel i highly accurate. Keywor: VSC converter, rt, R approach, LC approach, State pace moel, Freuency canning. T. NTRODUCTON he traitional moel of VSC converter in many lectromagnetic Tranient (MT) imulator employ the ifferent ON an OFF reitance value to imulate the ifferent witching tate of the emiconuctor [1]. n thi approach, the GBT/ioe witche a in Fig. 1.a, are repreente by a mall reitance R on for the ON tate an a large reitance R off for the OFF tate a in Fig. 1.b. However, with thi approach, the amittance matrix in MT imulation change an nee to be re-factorize after a witching action. A long a the witching freuency i high, uch a the cae of two level VSC converter with Pule With Moulation (PWM), thi high freuency an time-cotly calculation make the real time implementation a challenge. An alternative LC approach wa evelope [1-2], which ue a mall inuctor L ( L branch) to repreent the ON tate an a mall capacitor C in erie with a reitor R ( RC branch) for the OFF tate, a in Fig. 1.c. Alo, the Thi work wa upporte in part by the NSRC an RTDS Technologie. Yi Qi an Aniruha Gole are with Department of lectrical an Computer ngineering, Univerity of Manitoba, Winnipeg, Manitoba, Canaa ( iy3@myumanitoba.ca). Hui Ding an Yi Zhang are with RTDS Technologie, Winnipeg, Manitoba, Canaa ( hui@myumanitoba.ca). Paper ubmitte to the nternational Conference on Power Sytem Tranient (PST217) in Seoul, Republic of Korea June 26-29, 217 converter i imulate with a much maller imulation time tep t a compare to the external ac ytem which ha a larger time tep t b. The parameter of the LC moel are electe a in (1). 2L = t R t 2C (1) The 2L / t an t /2C are the companion circuit euivalent impeance of the inuctor an capacitor in MT imulation. The incluion of R minimize the potential amping between the L an RC branch. With euation (1), it i guarantee that the circuit impeance of the L an RC branch are the ame, o that the witching from the ON to OFF tate oe not change the network impeance matrix. Thi eliminate the nee for impeance matrix re-factorization on witching; only the formula to calculate hitory term change. Hence, the imulation time for each time tep i reuce, allowing a maller time tep an better accuracy in real time imulation. When it come to funamental freuency (6Hz), the impeance of the OFF tate (the RC branch) i much bigger than the ON tate (the RC branch). a. GBT/Dioe Switch ON moe OFF moe b. R moel Roff Figure. 1. Two type of GBT moel L ON moe OFF moe c. LC moel Typical L an C are electe to be mall number, for the cae tuie in below ection, thee value are hown in Table. TABL TYPCAL RLC VALUS N LC MODL Component R C L Value 132ohm.17uF.15mH However, although the LC approach i highly efficient numerically, there i a concern that replacing the ON an OFF reitance with inuctance an capacitance, may excite puriou reonance. Thi paper invetigate thi iue by conucting a freuency can on a ytem containing a VSC converter moelle with the R an the LC approache uing an rt imulator from RTDS Technologie. From thi canning, the C R

2 PLL freuency impeance i extracte to reflect the converter characteritic hown to the network. At the ame time, an analytical expreion for the freuency repone i erive from a mall-ignal tate pace moel [3-5] of the converter a an approximate. The reult comparion between the R an LC type converter prove that the LC type moel i highly accurate.. TST SYSTM An example VSC converter with a imple ac an c ie ytem i contructe in rt a hown in Fig. 2. The converter i moelle either uing the fat LC approach or the lower an more conventional R approach. j U ju P jq j Uc Cc Rc c A. Static reference n thi work, a tatic network - [4] rotating at ource funamental freuency ω i choen a the reference. The phae locke loop i ue to track the ac voltage. The relative poition between the PLL an tatic i hown in Fig. 4. We chooe the angle ifference θ to have a nominal teay tate value of in thi paper, which i convenient for calculation an comparion. The tranformation of element between the two (upercript for tatic, p for PLL ) i: [ ] = [ coθ inθ p inθ coθ ] [ p] (2) Static L R PCC Lt Rt Cf Uc juc Cc -Uc Figure. 2. lectrical ytem Rc -c θ PLL Static Figure. 4. Poition of PLL an tatic Vc Vcref Vacref Vac U U - - Um V V ref ref m m ωpll - - ω m m T T Uc a. Meaurement filter an per unit proceing x8 x1 x1 RT RT U V x9 - V - x11 - θpll Vc Um DQ To ABC a b c Linearization give: [ ] = [ coθ inθ p inθ coθ ] [ p] [ inθ coθ coθ inθ ] [ p] θ (3) B. nfluence of ON an OFF reitance The previou work [3-5] take the ON reitance a an OFF reitance a infinite in analytical moeling. Here actual witch reitance value can be inclue to get a better reult of the amping. The witch tate for each of the R in the a phae leg of a three-phae converter i hown in Fig. 5. The reitance alternately take on value of R on an R off a ecie by two complementary PWM moulate waveform. The reulting ac ie waveform ha the ame hape a the upper PWM ignal an alternatively witche between U c an U c, where U c i the c capacitor voltage. p b. Decoupling control logic Figure. 3. Control ytem of Converter Uc R value Fig. 3 how the converter control ytem incluing a ecouple controller for the irect () an uarature () current, an a Phae Locke Loop (PLL) to ynchronize the controller to the ac voltage. The ytem ata i provie in the Appenix. A. Phae a Roff nvere Waveform PWM Wave Bae Component. ANALYTCAL MODL The analytical moel i evelope to get an inepenent analytical freuency repone of the converter impeance. Thi i later compare with a canning repone obtaine from imulation. The tate pace moel i ifferent from earlier reearch a it explicitly inclue the R on an R off reitance, which coul have a bearing on the amping performance. R value -Uc Roff Figure. 5. PWM witching tate for the witche Bae on Fig 5, we obtain the euivalent circuit for the

3 converter a in Fig. 6. The ac ie network i connecte through the R on to the moulate waveform of c voltage ( j ) U c ( an are the output of the control ytem coming from (29)), an through the R off to the invere moulate waveform eual to ( j ) U c. The poitive c ie i connecte to two current ource, which are the prouct of two ac current value (from Fig 6.a) an the PWM witching function, an the negative c ie i ymmetrical to the poitive ie. To AC ytem U ju j PCC on*on* j -(off*off*) onjon ( j)uc Lt Rt Uc juc Roff -( j)uc Cf offjoff a. uivalent circuit of AC ie with an Roff Uc Cc c Rc c b. uivalent circuit of DC poitive ie with an Roff Figure. 6. uivalent circuit of ac an c ie with R on an R off We can write the analytical euation for Fig. 6.a: C f t [U ω C f U ] [ ] [ U ω C f U ] = [ ] [ ] (4) L t t [ ] [ R t R c ω L t ] [ ω L t R t R c ] = [ U U ] [ ] U c k (5) [ on 2 [ ] U c R off [ ] ] = (6) on R off R on [ off 2 [ ] U c R on [ ] ] = (7) off R off R on Supercript inicate the tatic ; an, coming from (27), are the output of the control ytem. n (5), the k an R c value are: k = (R off R on )/(R off R on ), R c = R off R on. The analytical euation for Fig. 6.b: C c U c t = ([ on ] [ off on ]) T [ off ] c (8) C. State pace moel The tate pace moel i obtaine by linearizing the euation: (2-8), an (14-29). t i eay to get the form: { = A B U (9) Y = C D U With thi tate pace moel the freuency impeance coul be conucte. However, it ha to be pecifie that the analytical moel i an approximate a it ue an average witching function to repreent the tranformation between ac an c ie of the converter. Thereby, the main purpoe of thi part i not a an accurate template for comparion, but a a anity check to the experimental reult. V. FRQUNCY SCANNNG The freuency canning metho [6] [7] wa introuce to tuy the mall ignal harmonic impeance of a Line Commutate Converter (LCC). A the MT moel of the LCC ytem i contructe, a harmonic current (or voltage), containing everal eui-magnitue freuency component a given by (1) i injecte at the noe at which the impeance of the ytem i eire. The injecte component have a very mall magnitue mag, o a not to affect the operating point of the ytem. n orer to prevent bunching in the time omain waveform, a non-linear phae hift i ae to each inuoial component [6]. The correponing voltage (or current) i meaure an it harmonic component extracte uing the Dicrete Fourier Tranform (DFT). Diviing the reultant voltage (current) component by mag give the impeance (amittance) at each freuency. fmax inj (t) = mag co(2πft k inj f 2 ) f=fmin (1) The canning can be one in the - omain or phae (abc) omain a icue later. A. mpeance looking from ac an c ie The impeance looking from the ac an c ie are both meaure by uitable injection a hown in Fig. 7. mpeance een from AC ie: [Z, Z, Z, Z ] PCC AC ie Lt Cf Rt a. impeance een from AC ie Cc Cc DC ie DC ie mpeance een from DC ie: Zc b. impeance een from in AC ie Figure. 7. mpeance to be canne from ac an c ie For the ac ie, a hown in Fig. 7.a. the impeance i meaure from the Point of Common Coupling (PCC) bu. Hence, the impeance can inclue the ac capacitor branch an the reflecte impeance of the c ie a een through the converter ac ie. The mall ignal virtual current injection to the ac capacitor an converter branch i et a input of the ytem, an the mall ignal voltage output in PCC bu i et a output. A in Fig. 7.b, for the c ie, the impeance meaurement inclue the c capacitor bu, in parallel with the reflecte

4 mpeance Magnitue (PU) mpeance Magnitue (PU) mpeance Magnitue (PU) mpeance Magnitue (PU) impeance of the ac ie viewe through the converter c terminal. B. njection ignal n practical canning, one can ue either current or voltage injection. A pecifie in [8] [9], the perturbation injection location nee not be at the location where the impeance or amittance nee to be meaure. n that cae, one imply ivie the DFT component of the voltage (current) an current (voltage) at the location of interet to get the impeance (amittance). n thi paper, for convenience, we chooe to inject a voltage. C. -- omain t can be hown that if phae coorinate are ue to obtain a freuency repone, there can be coupling in the freuencie. For example, if a poitive euence current of freuency i injecte into the converter at it ac bu, meaure voltage on the bu will inclue a poitive euence component at freuency, a well a a negative euence component at freuency -, where i the funamental freuency [1]. However, if the circuit i repreente in -- coorinate, the coupling between freuencie iappear [3]. But a coupling can till exit between the an uantitie. uation (11) i ue to tranform between phae a-b-c an - - coorinate. [ ] = 2 [ 3 coθ t co (θ t 2 3 π) co (θ t 2 3 π) inθ t in(θ t 2 3 π) in (θ t 2 3 π) 1/2 1/2 1/2 coθ t inθ t 1 a ] [ b ] c (11) a [ b ] = [ co (θ t 2 π) in(θ 3 t 2 π) 1 3 ] [ ] { c co (θ t 2 π) in(θ 3 t 2 π) 1 3 Where the reference angle θ t = ω t θ. The ω t i for tatic rotating, an the offet angle θ i ue to enure that U =. There i no zero-euence current flow path, we have =. Hence, the canning in thi paper oe inject only an irection current. To o thi, the an axi voltage injection are electe in the form (1), an then the phae injection (v a, v b, v c ) are calculate uing (11) an injecte into the network in the imulation. Again, a -- tranformation i applie to the meaure phae current to get - component an then the freuency component are obtaine uing a DFT. Once we have the freuency component of current an voltage, the amittance or impeance i reaily calculate by iviion. The ac ie impeance uner - omain i a 2*2 im matrix: Z ac (ω) = [ Z (ω) Z (ω) Z (ω) Z (ω) ] (12) To obtain the four impeance in (12), we firt inject voltage an oberve the reultant an irection current (i _1 (ω), i _1 (ω)) an voltage (v _1 (ω), v _1 (ω)). We then inject a ifferent ratio of - irection current, then the reultant current (i _2 (ω), i _2 (ω)) an voltage (v _2 (ω), v _2 (ω)) i meaure. The impeance can then be obtaine from (13). [ Z (ω) Z (ω) Z (ω) Z (ω) ] = [v _1(ω) v _2 (ω) ] [ i 1 _1(ω) i _2 (ω) v _1 (ω) v _2(ω) i _1 (ω) i _2 (ω) ] (13) D. Meauring The ampling time tep an ampling winow of voltage an current epen on the freuencie injecte. The ampling winow houl alway bigger than a cycle of any freuency in the injecting erie. When the ytem contain ome high freuency harmonic a the backgroun noie, a low pa igital filter i ue to pre-proce the ample ata. V. RSULT OF FRQUNCY MPDANC A. Sytem etting The freuency canning i employe on both the R approach an the LC approach converter in rt. n the R approach converter, the ON an OFF reitance value are: R on =.2PU, an R off = 2PU. Thee value are alo applie in the analytical moel. The imulation are conucte with a time tep of 5 for the external network an 5 n for the converter moel. Coniering that the freuency characteritic of the impeance for the VSC converter (no matter looking from ac or c ie) epen on the operating point, two typical operating point are choen in thi paper for comparion, a in Table, with ifferent active an reactive power from the PCC bu to the converter, a hown in Fig. 2. TABL OPRATNG PONTS Operating point P Q 1 1 PU PU 2.6 PU.2 PU B. mpeance comparion in operating point 1 At operating point 1, the VSC i operating at maximum active power. The comparion of ac an c impeance can for the R moel, the LC moel an the analytical reult i hown in Fig. 8 to 1, in the freuency range 1 Hz to 1 Hz, which i enough for mot of the network tability tuie Figure. 8. Ac ie impeance magnitue (Z Z Z Z)

5 mpeance Magnitue (PU) mpeance Magnitue (PU) mpeance Magnitue (PU) mpeance Magnitue (PU) mpeance Magnitue (PU) mpeance Magnitue (PU) n Fig. 8 to 9, the four ubplot are the - omain couple impeance looking from the ac ie: Z, Z, Z an Z (ee Fig. 7.a). Fig. 8 how the magnitue repone (in per unit) an Fig. 9 how the phae angle (in egree). Fig. 1 how the magnitue (in per unit) phae angle (in egree) of the impeance looking from the c ie: Z c (ee Fig. 7.b). From thee curve, it i eaily foun, the canne reult an the analytical reult match very well Figure. 9. Ac ie impeance phae angle (Z Z Z Z) Figure. 1. Dc ie impeance magnitue an phae angle C. mpeance comparion in operating point Fig are the magnitue an phae angle of impeance looking from the ac ie an Fig. 13 how the reult looking from the c ie. Thi impeance repone i alo obtaine from a imulation with 5 large time tep for external network (2 for converter network) in rt. n thi operating point, the impeance reult alo match very well, which mean the LC approach moel i alo reliable at thi operating point. At the ame time we coul alo make the ame comparion tep for the freuency repone uner other operating point, it i not lite in thi paper ue to the page retriction Figure. 11. Ac ie impeance magnitue (Z Z Z Z) Figure. 12. Ac ie impeance phae angle (Z Z Z Z) Figure. 7. Dc ie impeance magnitue an phae angle

6 V. CONCLUSONS AND DSCUSSONS Thi work invetigate the impeance characteritic of the converter moel in rt (both R an LC approach type), with a view to valiating the LC moel. Uing etaile MT imulation on the rt of a VSC-HVDC converter with realitic control, experimental freuency can are conucte on the R an LC moel with the converter operating at two ifferent operating point. The comparion between thee two impeance reult, a well a the analytical reult, how that the LC moel ha very goo accuracy, making it a goo choice for real-time imulation. n thi paper, we are mainly icuing on the pecific LC type 2-level VSC moel on the rt platform. Moreover, for the recently evelope Moular Multilevel Converter (MMC), a long a the internal etail are ignore, for the average value moel uing the ame witching function, much of the external behavior i probably till preictable uing the reult of thi paper [11]. V. APPND A. Sytem an Controller Data The electrical ytem parameter in Fig. 2 are a follow: TABL CRCUT DATA OF LCTRCAL SYSTM Parameter Value Parameter Value Ac bae voltage (L-L RMS) 1kV L.26526H Dc bae voltage 1kV R t 1ohm Sytem bae Mva 3MVA L t.13263h C f μF C c 1μF R 2ohm The c ie reitance R c i ubject to the operating point an we chooe a pure reitive loa for c ie ( c i if no voltage injection). Then the impeance characteritic woul not be ignificantly affecte by thi reitance (a mall reitance woul hort circuit the c capacitor). For the control ytem in Fig. 3, the parameter are: TABL V CONTROL SYSTM DATA Parameter Value Parameter Value T 3.2 K p3 1 T 4.2 K p4 2 T 5.4 K p5 1 T 6.4 K i T 7.5 K i2 5 T pll.5 K i3 1 K p1 2 K i4 5 K p2 2 K i5 1 B. Moel The ifferential euation for the analytical moel for the ytem beie the converter part are hown below (upercript for tatic, p for PLL ). For the ac ytem R-L branch, the euation: L t [ ] [ R ω L ] [ ω L R ] = [ ] [ U U ] (14) The voltage an current meauring proce, a well a the ecoupling control ytem: T v V c = U c V c (15) T v V = U p V (16) T v V = U p V (17) T i m = p m (18) T i m = p m (19) ref = K i2 (V cref V c ) K p2 (V cref V c ) (2) = V ω L t m R t m K i3 ( ref m ) K p3 ( ref m ) (21) ref = K i4 (V acref V 2 V 2 ) K p4 (V acref V 2 2 V ) (22) = V ω L t m R t m K i5 ( ref m ) K p5 ( ref m ) (23) The PLL: [ U p U p] = [ coθ inθ inθ coθ ] [U U ] (24) T pll U m = U p U m (25) ω = K i1 U m K p1 U m (26) θ = ω (27) The tranformation from the output of control ytem to tatic : [ ] = [ coθ inθ inθ coθ ] [ ] (28) The c ie R branch ( c i ): c = U c R c (29) V. RFRNCS [1] RTDS Technologie, Real time igital imulation for the power inutry manual et, Winnipeg, Canaa, 26. [2] Trevor Maguire an Jame Giebrecht, Small Time-tep (<2uSec) VSC Moel for the Real Time Digital Simulator, Proceeing of PST 25, Montreal Canaa, June 25, Paper No. PST c. [3] J. Z. Zhou, H. Ding, S. Fan, Y. Zhang an A. M. Gole, "mpact of Short- Circuit Ratio an Phae-Locke-Loop Parameter on the Small-Signal Behavior of a VSC-HVDC Converter," Tranaction on Power Delivery, vol. 29, no. 5, pp , Oct [4] L. Zhang, Moeling an control of VSC-HVDC link connecte to weak ac ytem, Ph.D. iertation, School of lect. ng., Royal ntitute of Technology, Stockholm, Sween, 29. [5] S. Arunpraanth, U. D. Annakkage, C. Karawita an R. Kuffel, "Generalize Freuency-Domain Controller Tuning Proceure for VSC Sytem," in Tranaction on Power Delivery, vol. 31, no. 2, pp , April 216. [6] iao Jiang an A. M. Gole, "A freuency canning metho for the ientification of harmonic intabilitie in HVDC ytem," in Tranaction on Power Delivery, vol. 1, no. 4, pp , Oct [7]. Papic an A. M. Gole, "Freuency repone characteritic of the unifie power flow controller," in Tranaction on Power Delivery, vol. 18, no. 4, pp , Oct. 23. [8] G. Franci, R. Burgo, D. Boroyevich, F. Wang an K. Karimi, "An algorithm an implementation ytem for meauring impeance in the D-Q omain," 211 nergy Converion Congre an xpoition, Phoenix, AZ, 211, pp [9] B. Wen, D. Boroyevich, P. Mattavelli, Z. Shen an R. Burgo, "xperimental verification of the Generalize Nyuit tability criterion for balance three-phae ac ytem in the preence of contant power loa," 212 nergy Converion Congre an xpoition (CC), Raleigh, NC, 212, pp [1] M. Mohae, A. M. Gole an S. lez, "Steay tate freuency repone of STATCOM," in Tranaction on Power Delivery, vol. 16, no. 1, pp , Jan 21. [11] T. Li, A. M. Gole an C. Zhao, "Harmonic ntability in MMC-HVDC Converter Reulting From nternal Dynamic," in Tranaction on Power Delivery, vol. 31, no. 4, pp , Aug. 216.