Grid Impedance Estimation for Islanding Detection and Adaptive Control of Converters

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1 Grid Impdanc Estimation for Islanding Dtction and Adaptiv Control of Convrtrs Abdlhady Ghanm, Mohamd Rashd, Mark Sumnr, M. A. El-says and I. I. I. Mansy Dpartmnt of Elctrical and Elctronics Enginring, Univrsity of Nottingham, Nottingham, UK. Elctrical Enginring Dpartmnt, Mansoura Univrsity, Mansoura, Egypt. Kywords: Grid impdanc stimation, SVPWM, Islanding dtction, Adaptiv control. Abstract Th grid impdanc is tim varying du to th changing structur of th powr systm configuration and it can hav a considrabl influnc on th control and stability of grid connctd convrtrs. This papr prsnts an onlin grid impdanc stimation mthod using th output switching currnt rippl of a SVPWM basd grid connctd convrtr. Th proposd impdanc stimation mthod is drivd from th discrtisd systm modl using two conscutiv sampls within th switching priod. Th stimatd impdanc is usd for islanding dtction and onlin currnt controllr paramtr adaptation. Thortical analysis and MATLAB simulation rsults ar prsntd to vrify th proposd mthod. Th ffctivnss of th grid impdanc stimator is validatd using xprimntal rsults. I. Introduction An incrasing numbr of powr lctronic convrtrs ar bing usd to connct rnwabl nrgy sourcs to th grid. In rcnt yars ral-tim grid impdanc stimation has bn rsarchd to improv controllr stability and protction (islanding dtction) in ths typs of convrtr [] [3]. Mthods for grid impdanc stimation ar gnrally classifid as passiv (non-invasiv) and activ (invasiv) [4]. Passiv mthods us th non-charactristic (harmonic) voltag and currnt masurmnts inhrntly prsnt in th systm to stimat impdanc whilst activ mthods dlibratly crat a disturbanc in th grid and th impdanc is stimatd from th grid rspons: in gnral good rsults can b achivd as th injction givs th masurmnts usd for impdanc stimation a high signal to nois ratio (SNR). Passiv mthods ar prfrrd as thy do not crat additional disturbancs in th grid, howvr th SNR is much lowr and th stimat tnds to b poorr. Svral activ tchniqus hav bn rportd in rcnt yars. Ciobotaru t al. [4] prsntd an onlin impdanc stimation tchniqu basd on priodical variations of activ and ractiv powr (PQ variations) of th grid connctd singl phas powr convrtr. In [5, 6] a currnt spik is dlibratly injctd at th point of common coupling (PCC) by a grid connctd convrtr. Basd on th voltag rspons to this disturbanc, th grid impdanc valu is dtrmind using Fourir transforms. A similar mthod mploying th Continuous Wavlt Transform (CWT) to driv th impdanc from transint data is prsntd in [7]. Asiminoai t al. [8] hav usd a PV invrtr to injct a low frquncy non-charactristic harmonic currnt of 75 Hz by adding a harmonic voltag to th voltag rfrnc of th PV invrtr. A Discrt Fourir Transform (DFT) amplitud and phas calculation is thn prformd to calculat th grid impdanc at that frquncy. In [9] an injction of a high frquncy signal comprising on or two voltag harmonic signals is implmntd. Th singl harmonic injction uss a 500 Hz signal and th doubl harmonic injction uss a 500 Hz and 600 Hz signals. Th authors in [0], prsntd a powr ntwork paramtr stimation basd on stimulations injctd through a puls width modulator, it crats a stimulation signal basd on Psudo Random Binary Squncs (PRBS) which hav bn usd to crat harmonic-rich stimulation. Good impdanc stimation can b achivd using th aformntiond activ mthods; howvr, thy suffr from a crtain numbr of problms. Ths problms ar mainly rlatd to th rat and amplitud of th rpatd injctions which ar usually kpt high to incras th SNR and advrsly incras th total harmonic distortion. In addition, th stimatd impdanc accuracy dpnds on th background harmonics. In [], a passiv grid impdanc stimation mthod basd on th inhrnt switching fatur (high frquncy harmonics) of th grid-connctd powr convrtr is prsntd. This mthod achivd fast and accurat impdanc stimation. Howvr, th currnt at th switching frquncy is vry small, so mor considrations for SNR and small currnt masurmnt ar rquird. A grid impdanc stimation mthod basd on th xcitation of th LCL-filtr rsonanc is prsntd in []. Th prsntd tchniqu is basd on th fact that th frquncy pak du to th rsonanc is particularly snsitiv to th grid impdanc chang. Th limitations of this mthod ar how to xcit th systm rsonanc in a controlld way and th high numbr of calculations can ovrload th procssing platform. In [3], an Extndd Kalman Filtr (EKF) is usd to stimat th tim variant grid impdanc. Th main disadvantag of this mthod is th complicatd tuning procsss for th covarianc matrics. Anothr xampl of a passiv mthod [4] is an analytical stimation modl cratd in th stationary rfrnc fram to stimat th total inductanc sn by a variabl switching frquncy convrtr using two conscutiv currnt sampls. Howvr, th stimatd inductanc is snsitiv to systm rsistanc. In this papr, an improvd approach to passiv impdanc stimation is proposd. It uss closd form modls for grid inductanc and rsistanc stimation drivd from th discrtisd systm modl in a rotating rfrnc fram. It uss

2 two conscutiv sampls within th switching priod of a SVPWM basd convrtr it could b argud that it is using th PWM itslf as an injction signal to obtain th bnfit of improvd SNR compard to most passiv mthods. Th nw inductanc stimator is compltly indpndnt from th rsistanc stimator. This papr is organizd as follows. In sction II, th systm dscription and control schm for a grid connctd convrtr ar prsntd. Sction III prsnts th drivation of th inductanc and rsistanc stimation modls. MATLAB basd simulation rsults for diffrnt scnarios and applications of th stimatd inductanc ar givn and discussd in sction IV. Exprimntal rsults ar prsntd in sction V and finally conclusions ar discussd. II. Systm Dscription A thr-phas grid connctd convrtr systm is shown in Fig.. Th powr convrtr is connctd to th PCC via an inductiv filtr. Th convrtr is opratd in currnt control mod with a snsorlss approach to grid voltag dtction. θ PLL is abc ω -st ω s ω -st θ - st Fig. : Thr-phas grid connctd convrtr tst systm. Currnt control loop Th currnt control loop with a snsorlss grid voltag dtction basd on a Phas Lockd Loop (PLL) is shown in Fig.. Th rror btwn th rfrnc and actual masurd currnts in a dq rotating rfrnc fram (synchronisd to th grid voltag vctor) is procssd via a PI controllr (togthr with cross coupling compnsation) in ordr to achiv indpndnt control of activ and ractiv powr and calculat th rquird convrtr output rfrnc voltag. A SVPWM tchniqu is usd to driv th powr convrtr switchs. i d v g v d-pi vd is abc rfrnc fram, so it is important to xtract th synchronizing angl vn if th voltag at PCC is highly pollutd du to th prsnc of a larg grid impdanc. To ovrcom this problm, a snsorlss grid voltag dtction basd PLL is usd [6]. Th output voltag from th PI controllr of th quadratur axis currnt control loop rprsnts th rfrnc quadratur axis componnt of th grid voltag and it can b usd for synchronization instad of PCC voltag masurmnt. Th PLL is lockd by stting to zro as a phas dtctor. A PI controllr is usd to control this componnt by minimizing th phas rror. Th output of th PI controllr is addd to a constant valu which rprsnts th nominal frquncy and hnc th output is th grid voltag frquncy. A Voltag-Controlld Oscillator (VCO), normally an intgrator, is thn usd to xtract th grid phas angl (s Fig. ). For th impdanc stimator, anothr slow PLL is usd as shown in Fig.. Th output grid voltag angl from th PLL is fd to a slow PLL and is xtractd. is usd to transform th abc currnt and voltag to th dq rotating rfrnc fram usd in impdanc stimation only whil is usd within th currnt controllr procsss and grid synchronization. Spac vctor PWM Fig. 3 shows a rprsntation of th basic spac-vctor and th rfrnc voltag vctor in th stationary rfrnc fram. It can b sn that th grid connctd convrtr shown in Fig. has ight switching stats to whr to ar nonzro voltag vctors form th axs of th hxagon and ach 60 shift, whil and ar zro voltag vctors locatd at th origin [7]. Th objctiv of th spac vctor tchniqu is to approximat th rfrnc voltag vctor with th ight spac vctors availabl in VSI. For instanc, if lis btwn two arbitrary vctors,, only th narst nonzro vctors (, ) and on zro vctor ( or ) should b usd. Fig. 4 shows th spac vctor implmntation in sctor on as an xampl. V 3 β ω V is abc J θ i d i q i q v q-pi v q J θ v abc V 4 V 7, 8 θ Vc V α ω ω Fig. : Currnt control loop with snsorlss PLL. ω s θ It should b notd that PLL basd synchronisation mthods mainly dpnd on th voltag at th PCC and thir dynamic rsponss advrsly affct th ovrall systm stability spcially in high impdanc ntworks [5]. In this papr, th grid impdanc stimator is basd on th currnt and voltag componnts masurd in th rotating dq V 5 V 6 Fig. 3: Basic spac vctor rprsntation. Th gnral xprssions for ach vctor tim at any sctor can b calculatd as [7]: =.. sin ()

3 =.. sin () = (3) = (4), = (5) Whr; T s is th sampling priod, s n is th sctor numbr which can b dtrmind according to th valu of convrtr rfrnc voltag position. III. Impdanc Estimation Mthod Th total inductanc and rsistanc (grid plus filtr) ar stimatd using two conscutiv currnt sampls masurd within th SVPWM priod and usd with th discrtisd systm modl in th rotating dq fram. For th grid connctd convrtr shown in Fig., th continuous-tim modl in th dq fram is: = (6) Whr subscript dq dnots th axs of an arbitrary rotating dq fram. c and g rfr to convrtr and grid rspctivly. Fig. 4 shows typical PWM outputs in sctor on and th thr fixd masurmnt instants in ach sampling priod, which ar markd as k- at th bginning, k- at T s /4 and k at th middl of th sampling priod. It should b notd from Fig. 4 that th convrtr output phas voltag wavforms ar constant during th tim intrvals of th voltag vctors V and V, which.g. for V ar qual to v an =V dc /3, v bn =-V dc /3 and v cn =-V dc /3. Howvr th quivalnt instantanous dq voltag componnts during ths tim intrvals ar tim varying, (s v d wavform in Fig. 4). Thrfor, th discrt form of (6) is givn in (7 and 8), whr subscript av dnots avrag valu,.g. th discrt voltag is th avrag valu of th instantanous voltag wavform v cdq (t) ovr th tim intrval btwn th sampling instants k- and k. Th currnt drivativs in (6) ar approximatd using th Forward Eulr mthod. Th discrt modl of (6) for two conscutiv sampls k and k- is xprssd as: = (7) = (8) Whr; =0.5 =0.5 (9) (0) = () v dc v dc T z 4 T T T s T z T T T z 4 Vz V V Vz V V Vz k Ts 4 Ts k k Fig. 4: SVPWM and masuring instants. =0.5 () Th grid voltag is assumd to b slowly varying, so for two conscutiv sampls, th v gdq componnts ar assumd constant in (7 and 8) and th discrt modl can b rarrangd as: = 4 (3) = 4 (4) Th discrt modls of th two conscutiv sampls givn in (3 and 4) ar analytically solvd for th unknown paramtrs (/L) and (R/L) whr R and L ar th total rsistanc and inductanc of th systm. = (5) = (6) 3

4 Aftr som algbraic manipulation, th solution for th unknown (/L) and (R/L) ar givn by (5, 6) as shown at th bottom of th prvious pag. It is worth noting that th drivd inductanc and rsistanc stimator modls ar fully dcoupld and indpndnt. It should b notd that th (R/L) stimator givn by (6) is mainly dpndnt on th voltag diffrnc and currnt drivativs btwn two conscutiv sampls. It mans thr is a high snsitivity to inaccurat masurmnts and avraging which will vntually lad to inaccurat stimats. Thrfor, in th following sctions only th inductanc stimator is invstigatd. An important practical issu that affcts th accuracy of currnt masurmnt during th switching priod is th high frquncy currnt ringing that happns aftr turn on/off switching instants [8] du to parasitic inductancs and capacitancs within th powr lctronic systm. In ordr to mitigat this problm, th stimation is disabld if th on/off instants hav occurrd lss than 5 µs bfor th masuring instants (to allow th ringing to dcay). IV. Simulation Rsults Th grid connctd convrtr shown in Fig. has bn modlld in MATLAB using paramtrs listd in tabl (I). A random whit Gaussian nois was addd to th masurd currnt to rflct ralistic masurmnt nois and th inductanc stimation (5) is prformd alongsid th simulation. symbol maning valu R f Filtr Rsistanc 0. Ω L f Filtr inductanc 4.3 mh R g Grid Rsistanc 0.3 Ω L g Grid inductanc 0.36 mh V g Grid voltag 400 V V dc DC-link voltag 700 V f s switching frquncy 0 khz Tabl (I): systm paramtrs. grid inductanc with insnsitivity to rsistanc variations. Th ramp in th stimatd inductanc is du to th rat limit applid to rduc th ffct of nois and masurmnt filtring. Fig. 5-b shows th instants at which th inductanc stimation is disabld to avoid th switching instant ringing/oscillation. Islanding dtction tst On important application of th grid inductanc stimation is islanding dtction. A simulation scnario for th us of inductanc stimator for islanding dtction is givn in Fig. 6 and th rsults ar shown in Fig. 7. i conv Fig. 6: Islanding tst systm configuration. Th convrtr is connctd to a grid mad up of two connctions; on is strong and th othr is wak. Th strong connction in Fig. 6 is disconnctd at t = 0. s and th stimatd inductanc changs to a highr valu (s Fig. 7-d) within 50 ms two supply priods. This is fast nough for th chang in th stimatd inductanc to b usd as a flag for islanding. i g -m i g -w Fig. 7: Simulation rsults for islanding dtction. Fig. 5: (a): Th stimatd inductanc. R g = 0.3 Ω for t < 0. s and R g = 0.5 Ω for t 0. s. (b): Zoom in shows stimation idl instants. Figur 5 shows th simulation rsults for systm inductanc stimation with diffrnt grid impdanc paramtrs. Th grid rsistanc is changd at t = 0. s from 0.3 Ω to 0.5 Ω and th grid inductanc is incrasd at t = 0. s from 0.36 mh to mh. Th rsults show accurat stimation of th chang in Adaptiv currnt control In this sction, th stimatd inductanc is usd for onlin currnt control loop adaptation. Th simplifid block diagram of th currnt control loop is shown in Fig. 8 and th closd loop transfr function is givn by (7). I K K s p i - V /(L sr) Fig. 8: Simplifid block diagram of th currnt control loop. = = I (7) 4

5 Th scond ordr systm givn by th closd loop transfr function has undampd natural frquncy of = and damping ratio of =0.5.. Th controllr paramtrs K p and K I ar adaptivly calculatd to achiv a spcific bandwidth and damping ratio basd on th stimatd inductanc. Th magnitud of th closd loop transfr function is st to b -3dB at th rquird bandwidth and damping ratio as givn by (8, 9). = = (8) = (9) Equation (8) is solvd using th Nwton-Raphson itrativ mthod for K p and thn K I is calculatd using (9) to achiv a bandwidth of 00 Hz and damping ratio of 0.8. Th adaptiv paramtrs ar updatd onc vry sampling priod and th sam PI paramtrs ar usd for both th d and q currnt loops. Th adaptation of th PI paramtrs du to chang of th grid inductanc is prsntd in Fig. 9. It can b sn that, at t = 0.05 s th grid inductanc is incrasd to mh giving a total inductanc of 6.3 mh. During th chang of th stimatd inductanc th PI paramtrs ar also adaptd to achiv th spcifid bandwidth and damping ratio. Onc th nw inductanc is stimatd and bcoms constant, th PI paramtrs also bcom stadily. Obviously, it can b sn that without th PI paramtr adaptation, an incras in th grid inductanc affcts th prformanc of th controllr and dcrass its bandwidth. In contrast, with th adaptiv PI controllr, th sam stp rspons bfor and aftr th grid impdanc chang is achivd. V. Exprimntal Rsults To validat th proposd impdanc stimator, th currnt and voltag wavforms of a thr-phas grid connctd convrtr wr capturd and procssd. Th convrtr was connctd to a Programmabl Voltag Sourc (PVS) via a L- filtr and controlld in rctifir mod using Txas Instrumnts TMS30C673 DSK fittd with th Actl FPGA A3P400 basd board. Th output lin voltag of th PVS was adjustd at 5 V, th dc-sid was st at 00 V and a switching frquncy of khz was usd (th switching frquncy is low as th rig is part of anothr projct invstigating mdium voltag switching circuits). Th thr-phas currnts and thr PWM lin-to-lin voltags wr capturd and stord for.5 cycls using two synchronizd LCroy oscilloscops. Th currnt and voltag signals wr sampld at 5 MHz and 50 MHz rspctivly. Th thr-phas lin-to-nutral voltags wr xtractd from th masurd thr-phas lin-to-lin voltag as: =, =, = (0) On cycl of masurd thr-phas currnts at th input of th convrtr and th xtractd thr-phas lin-to-nutral voltags ar givn in Fig.. Fig. 9: Adaptation of PI paramtr with grid inductanc variation. Fig. : (a): Thr-phas supply currnts. (b): Thr-phas lin-to-nutral voltags. Th tim stp rspons at diffrnt grid inductanc valus without and with th adaptiv PI controllr for d -axis control loop is prsntd in Fig. 0. Fig. : Estimatd inductanc. Fig. 0: d-axis stp rspons. Th currnt and phas voltag masurmnts wr procssd offlin using th inductanc stimator modl givn in (5) and th stimatd inductanc rsult is shown in Fig.. It can 5

6 b sn that th avrag valu of th stimatd inductanc is 0.3 mh. An FFT was applid to th masurd currnt and phas voltag and th inductanc was calculatd using th switching frquncy sidband frquncis as 0.6 mh which is closd to th stimatd valu, dmonstrating th ffctivnss of th proposd impdanc stimator. VI. Conclusion In this papr, closd form grid inductanc and rsistanc stimation modls wr drivd from th discrt grid connctd convrtr modl in th dq rfrnc fram. Th stimators us two conscutiv currnt sampls masurd within th SVPWM switching priod. Th drivd inductanc and rsistanc stimator modls ar fully dcoupld and indpndnt. Th ffctivnss of th proposd stimation approach for islanding dtction and adaptiv tun (onlin) of th PI currnt controllr gains ar vrifid by simulation. Exprimntal rsults dmonstrat th ffctivnss of th proposd impdanc stimator. Acknowldgmnts This work was supportd by Egyptian Govrnmnt-ministry of highr ducation (cultural affairs and missions sctor) PhD scholarship. Th authors would lik to thank Savvas Papadopoulos for supporting th xprimntal work. Th authors also gratfully acknowldg support from EPSRC through th IMASE projct (Rfrnc EP/K03697/). Rfrncs [] T. Strassr, F. Andrén, J. Kathan, C. Ccati, C. Bucclla, P. Siano, P. Litão, G. Zhablova, V. Vyatkin, P. Vrba, and V. Maˇrík, A rviw of architcturs and concpts for intllignc in futur lctric nrgy systms, IEEE Trans. Ind. Elctron., Vol. 6, no. 4, pp , Apr. 05. [] X. Guo, X. Zhang, B. Wang, W. Wu, and J. M. Gurrro, Asymmtrical grid fault rid-through stratgy of thr-phas grid-connctd invrtr considring ntwork impdanc impact in low-voltag grid, IEEE Trans. Powr Elctron., vol. 9, no. 3, pp , Mar. 04. [3] M. Sumnr, A. Abusorrah, D. Thomas, P. Zanchtta, Ral Tim Paramtr Estimation for Powr Quality Control and Intllignt Protction of Grid-Connctd Powr Elctronic Convrtrs, IEEE Trans. Smart grid, Vol. 5, no. 4, pp , Jul. 04. [4] M. Ciobotaru, R. Todorscu, P. Rodriguz, A. Timbus, and F. Blaabjrg, Onlin grid impdanc stimation for singl-phas grid-connctd systms using PQ variations, in Proc. 38th IEEE Powr Elctronics Spcialists Conf. (PESC), pp , Jun [5] B. Palthorp, M. Sumnr, and D. Thomas, Powr systm impdanc masurmnt using a powr lctronic convrtr, in Proc. of Harmonics and Quality of Powr, vol., pp. 08 3, 000. [6] M. Cspds and J. Sun, Onlin grid impdanc idntification for adaptiv control of grid-connctd invrtrs, in Proc. IEEE ECCE, Raligh, NC, USA, pp. 94 9, 0. [7] M. Sumnr, D.W.P Thomas, A. Abusorrah, and P. Zanchtta, Powr Systm Impdanc Estimation for Improvd Activ Filtr Control, using Continuous Wavlt Transforms, Proc. IEEE Powr Eng. Soc. Transmission Distribution Conf. Exhibit., pp , May -4, 006. [8] L. Asiminoai, R. Todorscu, F. Blaabjrg and U. Borup Implmntation and tst of an onlin mbddd grid impdanc stimation tchniqu for PV invrtrs, IEEE Trans. Ind. Elctron., vol. 5, no. 4, pp.36-44, 005. [9] M. Ciobotaru, R. Todorscu, and F. Blaabjrg, Onlin grid impdanc stimation basd on harmonic injction for grid-connctd PV invrtr, in Proc. IEEE ISIE,, pp , Jun [0] S. Nshvad, S. Chatzinotas, J. Sachau, Widband Idntification of Powr Ntwork Paramtrs Using Psudo-Random Binary Squncs on Powr Invrtrs, IEEE Trans. Smart grid, vol. 6, no. 5, pp , Sp. 05. [] H. Gu, X. Guo, D. Wang, and W. Wu, Ral-tim Grid Impdanc Estimation Tchniqu for Grid-Connctd Powr Convrtrs, IEEE Intrnational Symposium on Industrial Elctronics (ISlE), pp. 6-66, Hangzhou, 8-3 May 0. [] M. Lisrr, F. Blaabjrg and R. Todorscu, Grid Impdanc Estimation via Excitation of LCL-Filtr Rsonanc, IEEE Trans. on Industry Applications, vol. 43, pp , Sp [3] N. Hoffmann and F. W. Fuchs, Minimal invasiv quivalnt grid impdanc stimation in inductivrsistiv powr-ntworks using xtndd Kalmanfiltr, IEEE Trans. Powr Elctron., vol. 9, no., pp , Fb. 04. [4] B. Arif, L. Tarisciotti, P. Zanchtta, J. Clar, Grid paramtr stimation using modl prdictiv dirct powr control, IEEE Trans. on Industry Applications, vol. 5, pp , Nov. 05. [5] J.Z. Zhou, Hui Ding, Shngtao Fan, Yi Zhang, A.M. Gol, Impact of Short-Circuit Ratio and Phas- Lockd-Loop Paramtrs on th Small-Signal Bhavior of a VSC-HVDC Convrtr, Powr Dlivry, IEEE Transactions on, vol. 9, no. 5, pp , Oct. 04. [6] D. Li, Y. Notohara, Y. Iwaji, Y. Kurita, AC voltag and currnt snsorlss control mthod for thr-phas PWM convrtr, Wily Priodicals, Inc. Elctrical Enginring in Japan, vol. 7, no. 4, pp , Sp. 00. [7] Z. Shu, J. Tang, and J. Lian, An fficint SVPWM algorithm with low computational ovrhad for thr phas invrtrs, IEEE Trans. Powr Elctron., vol., no. 5, pp , Sp [8] A. E. Ginart, D. W. Brown, P. W. Kalgrn, and M. J. Romr, Onlin ringing charactrization as a diagnostic tchniqu for IGBTs in powr drivs, IEEE Trans. Instrum. Mas., vol. 58, no. 7, pp , Jul