Dscrete moel prectve reuency an voltage control o solate mcro-gr n smart gr scenaro Puvvula S R V R S S Vyasagar Electrcal engneerng epartment Inan Insttute o echnology Chenna, Ina ee4@ee.tm.ac.n Shant Swarup Electrcal engneerng epartment Inan Insttute o echnology Chenna, Ina swarup@ee.tm.ac.n Astract In an solate mcro-gr electroncally nterace DG (EI-DG unts shoul also partcpate n reuency an voltage control along wth synchronous generator ase DG (SG- DG unts to ensure power ualty an stalty o the mcro-gr. he conventonal way o controllng reuency an voltage s to alance actve power an reactve power o the system y mplementng roop characterstcs (P-, Q-V or EI-DG unts wth PI controllers an automatc generaton control (AGC an automatc voltage regulator (AVR or SG-DG unts. Wth the avent o smart mcro-grs, a centralze control or oth reuency an voltage usng moel prectve controller (MPC s an alternatve to the conventonal controllers. he optmzaton capaltes o MPC make t sutale or reuency an voltage control o mcro-grs euppe wth ast an relale communcaton. hs paper nvestgates the perormance o a centralze screte moel prectve controller (DMPC n an solate mcro-gr wth photovoltac (PV an esel generators. he small sgnal ynamc moels o the PV converter an SG-DG are consere n the esgn o the DMPC. he mcro-gr network an loas are represente usng steay state power alance euatons. he perormance o the DMPC s teste usng MALAB sotware package. eywors solate mcro-gr;moel prectve controller; small sgnal moel; reuency control; voltage control; roop characterstcs; I. INRODUCION Conventonal power systems wth large synchronous generator ase power plants mantans reuency an voltage stalty wth the help o automatc generaton control (AGC an automatc voltage regulator (AVR. AGC controls the necte actve power an AVR controls the exctaton an there y controls the necte reactve power []. Wth the avent o mcro-grs the aspects o reuency an voltage control are raply changng. A mcro-gr generally conssts o two or more strute generators. he generators may e o conventonal esel or steam type or electroncally nterace renewale sources. Voltage o the mcro-gr s locally controlle y generatng sucent reactve power where as reuency control s taken care y man gr n gr connecte moe [2][]. All the generators n mcro-gr operate as PQ sources generatng pre ene actve an reactve power set-ponts [2-4]. In solate mcro gr envronment oth synchronous generator ase (SG-DG an electroncally nterace strute generators (EI-DG are orce to partcpate n reuency regulaton an voltage control [4][5]. he conventonal way o controllng voltage an reuency n solate mcro-gr s to orce the EI-DG to ollow roop characterstcs (P-, Q-V through nepenent - current control usng PI controllers [2-6]. In smart gr scenaro, n the presence o ast communcaton evces moel prectve controller (MPC s an alternatve to the conventonal PI controllers or controllng voltage an reuency o solate mcro-grs. Usng present state normaton o a system, MPC prects the uture response o the system wth the help o a mathematcal moel o the system [7-9]. Whle controllng reuency an voltage many constrants are mpose on the operaton o the controller especally n solate mcro-grs whch can e hanle y the MPC very well when compare to the other controllers [8][9]. It can explot our knowlege aout the sturances that are aectng the reuency an voltage. hs s not the case wth presently use PI control methos. hs paper presents a etale approach o centralze reuency an voltage control o a photovoltac (PV an esel generator ase mcro-gr n solate envronment usng screte moel prectve controller (DMPC. he superorty o DMPC over conventonal PI controller s explane usng smulaton results. II. MAHEMAICAL MODEL OF MICRO-GRID A. Mcro-gr escrpton Mcro-gr use n the present stuy s compose o two generators, an EI-DG unt o 2.5-MVA an a SG-DG unt o 5-MVA capacty. he EI-DG unt represents PV source nterace wth the mcro-gr usng voltage source converter (VSC. SG-DG represents synchronous generator couple to turne wth esel as nput uel. he parameters o the two DG unts are gven n []. he normaton aout each o the component s shown n Fg.. For the ease o analyss the entre mcro-gr wth uses s represente y a three us system shown n Fg. 2. For esgnng the DMPC, mcro-gr lnearze moel s expresse n state space representaton as x Ax B u ( t 978--4799-54-/4/$. 26 IEEE
E ( x x E x xls E o E ( x x 2 t ( x xls ( Fg. Mcro-gr one lne agram o construct (, the ynamc moels o the EI-DG, SG- DG, mcro-gr network an loas are reure. In Fg., - s the gloal reerence rame whch s an magnary synchronous rame rotatng at the angular spee o ω. Intally -axs s orente along voltage space vector V G o us B. - s the reerence rame o SG-DG. It s locke to SG-DG rotor an rotates wth angular spee o ω r. axs s algne along machne nternal voltage E g. δ s the power angle o SG-DG an s relate to nstantaneous rotor angle δ o SG-DG y the euaton 2 (2 - s the reerence rame o EI-DG rotatng at the angular spee o ω. s always algne along the voltage space vector v G o B as shown n Fg.. δ s the nstantaneous phase angle o v G. B. SG-DG moel he SG-DG moel n - rame o reerence s represente y su transent moel o the synchronous generator wth stator transents neglecte. he turne moel wth reheater an nherent spee roop governor s consere n ths stuy. he exctaton system s a generc IEEE DCA system. he complete moel o the SG-DG n per unt (p.u. s gven y (-(9 Fg. 2 Reuce mcro-gr network E ( x x o E ( x x E x xls 2 t ( x xls 2 (4 2 (5 o E ( x xls 2 t (6 o E ( x xls t ( x xls ( x x (7 v rs x E ( x xls ( x xls ( x xls ( x x (8 v rs x E 2 ( x xls ( x xls r (9 t 2H r ( m e D ( r t E ( E VR ( E S E ( E E t VR A F V R E ( V V (2 A R A F A re t F RF F ( RF E t F m HPRH HPRH (4 RH m ( PCH PSV t CH CH PCH (5 CH PCH PSV t PSV (6 r SV PSV Pre ( t RD v V sn ( (7 v V cos ( (8 e v v (9 Where x, x represents - axs synchronous reactance. x, x represents - axs transent reactance an x, x represents - axs su-transent reactance. x ls s the stator leakage reactance. E, E are - axs nuce voltages. Ψ, Ψ 2 are the lux lnkages o amper wnngs o an axs. o, o are transent open crcut tme constants o - axs. o, o are su transent open crcut tme constants. v, v are the termnal voltage - components., are the - currents. H represents euvalent nerta o turne an synchronous generator rotors. D s the reuency epenent loas ampng constant. E s the el exctaton. RH, CH an SV are the reheater, steam chest an steam valve tme constants respectvely. RH s gan o reheater. P CH an P SV are the power outputs rom steam chest an steam valve respectvely. R D s the roop constant o the spee governor. P re s the reerence set pont o the turne moel. m an e are the mechancal an electromagnetc torues. E an E are excter gan an tme constant respectvely. R F s the rate
Q v v For, (27 G P Q For 2 (28 G G Where P G an Q G are generator actve an reactve power output at th us. P D an Q D are loa actve an reactve power eman at the th us. V an V are the voltages at th an th us. θ an θ are the phase angles o th an th us voltage wth respect to -axs. y s the (, element o the amttance matrx wth magntue Y an angle α. Fg. Reerence rames o mcro-gr eeack. A, A an V R are voltage regulator gan, tme constant an output voltage respectvely. F an F are eeack transormer gan an tme constant respectvely. V re s the reerence voltage o the regulator an V s the generator termnal voltage. C. Electroncally nterace strute generator moel EI-DG o Fg. 2 s a PV source connecte to B through a -Ф VSC. On AC se o the nverter, R s the p.u. value o on state swtchng losses, resstance o the nterace transormer an lter per phase. X represents p.u. value o lter nuctance an leakage nuctance o the nterace transormer per phase. he EI-DG moel n ts reerence rame s gven y R (2 ( e v t X X R (2 ( e v t X X Where v an v are - components o us voltage. an are - components o nverter current output. e an e are - components o the nverter output voltage. When axs s taken n such a way that t s orente along the voltage space vector o us, then v an v can e wrtten as v V (22 v (2 D. Mcro-gr network moel Snce the network ynamcs are ast when compare to the controller an generator ynamcs, network an loas n ths stuy are represente y (24 P P V V Y cos ( Q G G D Q D V V Y sn ( (25 P v v For, (26 G III. MODEL PREDICIVE CONROLLER FORMULAION A. MPC escrpton he man uncton o the MPC controller s to mantan reuency an voltage stalty o mcro-gr y mantanng reuency an voltage wthn lmts or the nput sturances. In the present stuy the sturances are small sgnal loa changes. Whle ormulatng the mathematcal moel o the MPC, numer o nputs an outputs o the mcro-gr are to e chosen as per the oectve o the stuy. In the present stuy t s the reuency an voltage control that s to e acheve wth MPC. he controller s a centralze controller an t reures the mcro-gr to e smart n nature wth ast ata communcaton prove. MPC computes traectory o controlle uture nputs o a plant to optmze the uture outputs usng the mathematcal moel o the plant. Precton horzon s the tme pero or numer o samples up to whch outputs are to e estmate y gvng plant state normaton at the startng tme o precton. he tme up to whch the uture traectores o the nputs are compute s calle control horzon. It ollows the receng horzon prncple so that only rst sample o the nput s gven as nput to the system an or the next samplng nstant the precton an receng horzon control repeats. he entre optmzaton s one wth regars to an oectve uncton. In Fg. 4 plant represents the mcro-gr. MPC lock contans normaton aout the mathematcal moel o the mcro-gr, oectve uncton J, precton horzon an control horzon. It computes the optmal system nput u over a xe control horzon. he rst sample o the nput u s gven as the nput to the plant an the process s contnue or other samples. y re contans set-ponts o the outputs. he loop s close y the measurements that nclue plant outputs y an measurale states. State estmaton lock s use to calculate the states whch are not measurale at each sample as the MPC nees complete state normaton x at the startng tme o precton horzon. B. Mathematcal ormulaton o the MPC he mcro-gr euatons rom (-(28 are o contnuous tme euatons. hey are to e converte nto screte tme an wrtten n the orm o x ( k A x ( k B u ( k B w( k (29 y sc sc ( k C sc sc x sc sc ( k sc w
part n ΔU opt that correspons to the present samplng nstant s taken as the nput vector an s apple to the plant. he process s repeate or the next samples. Fg. 4 MPC overvew Where x sc represents a vector contanng screte states o the mcro-gr, u s the control nput, y sc s the output vector o the plant. w s the nput loa sturance vector o the plant. (A sc, B sc, C sc s the state space trplet n screte orm. k s the samplng nstant. he screte moel s then converte nto mente state space moel o the orm Where x y sc ( k A x ( k B u ( k ( ( k C x ( k x (k = [Δx sc (k y sc (k ] Δx sc (k = x sc (k-x sc (k- Δu(k = u(k-u(k- rplet (A,B,C s calle mente moel o the plant. Now ene two vectors o the orm Y est U opt y sc ( k k u ( k k y sc ( k 2 k y sc u ( k k u ( k N C ( k N k P k ( Where y sc (k +m k s the precte output at m th sample rom the present sample k. Δu(k +m k s the optmze controlle nput at m th sample rom the present sample k. N P an N c are the precton horzon an control horzon. By manpulatng ( an ( Y est can e wrtten as Y est F x ( kgu (2 Hence rom (2 precte output up to N P samples rom k nstant can e wrtten wth the knowlege o the state varales at k sample an the optmze controlle nputs up to N c - samples rom k sample. he nal oectve uncton that etermnes the optmze control nput vector ΔU opt can e wrtten n the uaratc orm as J RS Yest ( RS Yest opt ( U PU ( Where R S s the output reerence set-pont vector whch contans the reerence set-ponts or the outputs o the plant. It s to e note that the reerence set-pont o a partcular output s constant throughout the precton horzon. P s the penalty actor on the nput varales. Ater optmzaton at each sample an optmze ΔU opt vector s generate an only that opt IV. RESULS AND EXPLANAION For the analyss o the capalty o DMPC, t s mplemente n the mcro-gr shown n Fg. 2. Mcro-gr erental an algerac euatons (DAE rom (2-(28 are lnearze aout an operatng pont. Operatng pont use or the present stuy s gven n APPENDIX. he lnearze algerac euatons are then manpulate n such a way that the complete moel o mcro-gr can e expresse wth the help o erental euatons only. By takng a screte tme step o 2ms, the mcro-gr moel s expresse n screte state space orm gven y (29. he nput an output vectors o the plant are Where G P G P G G u P re y P, re R D r e V e G n normal moe n reuency regulaton moe G represents the role o EI-DG n the mcro-gr. In steay state EI-DG generates constant actve power accorng to ts pre-set value P,re. Durng transent state t acts n reuency regulaton moe n whch t austs ts actve power accorng to ts roop characterstcs gven y R D. A. Perormance o MPC urng loa sturances n mcrogr A step loa change o 5kW at B s apple at 5 st samplng nstant as nput sturance whch s shown n Fg. 5. he output set-pont reerence vector (R S elements are taken as zeros. Control horzon an precton horzon are taken as 2 an 4 samples respectvely. he penalty actor P or every nput varale s taken as.. he reuency evaton o the system wth DMPC s shown n Fg. 6. he peak evaton occurre s 59.987 Hz whch s well wthn lmts o 59.9 Hz to 6. Hz. he reuency s restore to nomnal value n 7.4 sec. Fg. 7 shows the mechancal power output rom the turne o the SG-DG. In the steay state the mechancal nput o the SG-DG s ncrease y 5.8 kw rom 267.5 kw to 8. kw. Hence the total loa change s compensate y ncrease n the output power o SG-DG alone n the steay state. However urng transents loa change s alance y ncrease n mechancal output rom the esel turne, ncrease n power output o the EI-DG unt an energy store n the SG-DG nerta. Fg. 8 shows the actve power output o the EI- DG unt. Beore sturance EI-DG generates constant power output o 5 kw ase on ts reerence actve power setpont. Ater the sturance occurre, urng transent state t ollows the roop characterstcs assgne to t untl the reuency s completely restore. When the reuency s restore t agan swtches ack to ts normal moe n whch t ollows pre- assgne actve power set pont.
POWER (kw -AXIS CURREN OF EI-DG (p.u. -AXIS CURREN OF EI-DG (p.u. VOLAGE A BUS- (p.u. FREQUENCY (Hz VOLAGE A BUS- (p.u. LOAD CHANGE A BUS- (kw POWER (kw 6 5 4 2 6.5 2 4 5 6 7 8 9 6 Fg. 5 Loa sturance at us B 525 52 55 5 55 5 495 2 4 5 6 7 8 9.5 Fg. 8 actve power output o EI-DG 59.995 59.99 59.985 59.98 2 4 5 6 7 8 9 Fg. 6 Freuency o the mcro-gr.9995.999.9985 2 4 5 6 7 8 9 Fg. 9 shows the voltage at B. he peak voltage evaton s.9985 p.u. he voltage s restore to p.u. n 6 samples whch s.2 sec. he voltage s locally controlle y the EI- DG unt y generatng sucent reactve power. Hence DMPC s well sute or ast voltage recovery. Fg. shows the voltage at B whch s controlle y the local excter o SG-DG. Due to the slow ynamcs o the excter, voltage recovery at B s takng more tme than the tme taken y DMPC at B. Fg. an Fg. 2 show an o EI-DG. From Fg. t can e notce that current s the key parameter to control actve power output o the EI-DG. Beore an ater transent pero, s same ncatng that actve power output o the EI-DG s ollowng pre-assgne reerence n steay state an roop characterstcs n transent pero. Reactve power necte y EI-DG can e controlle y current. Hence y usng DMPC nepenent - current control can e acheve. Fg. an Fg. 4 compares PI control wth MPC n the context o reuency an voltage control o mcro-gr. ypcal parameters o PI control are gven n []. From Fg. an Fg.4 t can e notce that MPC ha a etter steay state perormance an transent perormance when compare to PI control..2.9998.9996.9994.9992.999 Fg. 9 Voltage at us B.9988 2 4 5 6 7 8 9.8.6.4.2. Fg. Voltage at us B.298 2 4 5 6 7 8 9 -.485 Fg. -axs current o EI-DG 2 -.49 29 -.495 28 27 26 2 4 5 6 7 8 9 Fg. 7 Mechancal nput o the SG-DG -.5 2 4 5 6 7 8 9 Fg. 2 -axs current o EI-DG
VOLAGE A BUS- (p.u. FREQUENCY (Hz 6.5 6 59.995 59.99 59.985 59.98 59.975 PI MPC 59.97 2 4 5 6 7 8 9.5.9995.999 Fg. Comparson o reuency control usng PI an MPC PI MPC.9985 2 4 5 6 7 8 9 Fg. 4 Comparson o voltage control at B usng PI an MPC B. Impact o storage on the system I the solate mcro-gr s euppe wth a storage system, then the reuency relate ssues can e hanle more eectvely. Generally urng schargng, storage an ts assocate nverter are orce to operate at unty power actor (UPF so that only actve power s necte nto the mcro-gr. Whle chargng t acts as UPF loa. Mathematcal moel o the MPC n the presence o the storage not change much except that two more states, - axs currents o storage nverter are ae to the mathematcal moel an the control s smlar to that o the PV nverter control. However the role o the storage urng a sturance n the system s ece y the state o charge (SOC. I SOC s wthn lmts then t s allowe to partcpate n reuency regulaton wth an emulate roop characters along wth other generators n the system untl ts SOC reaches ether maxmum or mnmum lmts epenng on the type o loa sturance. Once SOC reaches lmts, then t acts as controllale UPF loa. C. Possltes o practcal mplementaton he practcal harware mplementaton o the MPC n solate mcro-grs can e one usng A mcro-controller whch uses a gtal sgnal processor (DSP chp. hs can e mplementale or small mcro-grs wth lmte generators. For laoratory setups an or prototypng o real tme systems, MPC can e mplemente usng MALAB real tme workshop an xpc target. For large mcro-grs MPC can e mplemente usng a real tme computer ase montorng an supervsory control system nterace wth programmale logc controller. V. CONCLUSION he reuency an voltage control capalty o DMPC n solate mcro-gr s nvestgate n ths stuy. Dynamc moels o the mcro-gr generators are consere or the stuy. Mcro-gr network s represente y steay state euatons. Mathematcal euatons o the DMPC are gven n etal. Smulatons are carre out usng MALAB sotware package. Loa changes are taken as the nput sturances an the results shows that DMPC proves ast recovery o voltage an reuency. he results show that DMPC can coornate wth spee governor an exctaton o the SG-DG. Smulatons also show that the ynamc characterstcs o DMPC are etter than PI control. APPENDIX Operatng pont o the mcro-gr: V = V = p.u. V 2 =.997 p.u. P G =.26 MW Q G =.4652 MVAr P G2 =.5 MW Q G2 = 2.45 MVAr θ = θ 2 = -.297 θ = -.6747 REFERENCES [] P. unur, Power System Stalty an Control. New York, USA: McGraw-Hll, 994. [2] F. atrae, M. R. Iravan, an P. W. Lehn, Small-sgnal ynamc moel o a mcro-gr nclung conventonal an electroncally nterace strute resources, IE Gener. ransm. Dstr., vol., no., pp. 69 78, May 27. [] F. atrae, M. R. Iravan, an P. W. Lehn, Mcro-gr autonomous operaton urng an suseuent to slanng process, IEEE rans. Power Del., vol. 2, no., pp. 248 257, Jan. 25. [4] F. atrae an M. R. Iravan, Power management strateges or a mcrogr wth multple strute generaton unts, IEEE rans. Power Syst., vol. 2, no. 4, pp. 82 8, Nov. 26. [5] a Yu, Qan A, Shy Wang, Janmo N, an anguang Lv, Analyss an optmzaton o roop controller or mcrogr system ase on small sgnal ynamc moel, IEEE rans. Smart Gr, vol. 7, no. 2, pp. 695 75, Mar. 26. [6] C. Schauer an H. Mehta, Vector analyss an control o avance statc VAr compensators, IEEE Proc. C Gen. ransmss. Dstr., vol. 4, no. 4, pp. 299 6, Jul. 99. [7] L. Wang, Moel Prectve Control System Desgn an Implementaton Usng MALAB. Berln, Germany: Sprnger-Verlag, 29. [8] A. M. Ersal, I. M. Cecílo, D. Faozz, L. Imslan, an N. F. hornhll, Applyng moel prectve control to power system reuency control, n Proc. 2 4th IEEE/PES Innovatve Smart Gr echnologes Europe, 2. [9] A. M. Ersal, L. Imslan, an.uhlen, Moel prectve loareuency control, IEEE rans. Power Syst., vol., no., pp.777 785, Jan. 26. [] H. Xn, Y. Lu, Z. Wang, D. Gan, an. Yang, A New Freuency Regulaton Strategy or Photovoltac Systems Wthout Energy Storage, IEEE rans. Sustan. Energy, vol. 4, no. 4, pp. 985 99, 2.