1 Smart Grd Technologes for Reacte Power Compensaton n Motor Start Applcatons Maryclare Peterson, Member, IEEE and Brj N. Sngh, Member, IEEE Abstract Seeral major power outages hae been attrbuted to nsuffcent oltage support and subsequent oltage collapse. Aordngly, reacte power management has gan ncreased attenton for relablty mantenance of both transmsson and dstrbuton systems. In partcular, motor startng applcatons draw a large amount of reacte power and contrbute to system degradaton, partcularly n a weak area. Consequently, ths paper nestgates smart grd technologes for reacte power compensaton for motor startng applcatons n order to prode the necessary oltage support, reduce the nrush current, and decrease the motor startng tme. The two dynamc VAR deces that are proposed are the Statc Compensator (STATCOM) and Statc Synchronous Seres Compensator (SSSC). Detaled mathematcal models are deeloped for these deces as well as the proposed control logc. Smulaton results for STATCOM and SSSC-based compensators are proded to erfy the auracy of the deeloped models and control logc and obsere the effecteness of the dynamc VAR deces. Index Terms Reacte power, Statc compensators, Statc synchronous seres compensators. R I. INTRODUCTION eacte power compensaton s essental for satsfactory performance and relable operaton of AC power systems. Inadequate reacte power support leads to unaeptable system oltages and reduced ablty to transfer power from source to load. Under extreme condtons, nsuffcent VAR support may contrbute to oltage collapse and wde-area blackouts. Approprate reacte power compensaton technques prode such benefts as ncreased transmsson effcency through reduced losses, reduced grd congeston, ncreased transfer capablty, and enhanced grd relablty [1]. Reacte power compensaton technologes are dded nto two broad categores: statc VAR compensaton and dynamc VAR compensaton. Statc VAR deces are the most costeffecte; howeer, ther prmary constrant s that ther reacte power output s dependent on the square of the system oltage. Consequently, adequate reacte power compensaton may not be aalable when t s needed most at lower system oltages. Dynamc VAR deces are smart technologes, whch can be utlzed to prode fast reacte power support despte low oltage condtons. Ths paper demonstrates the effecteness of two smart Maryclare Peterson s wth Entergy Serces, Inc., New Orleans, LA 711 USA (e-mal: mpeter@entergy.com). 978-1-444-6547-7/1/$6. 1 IEEE technologes for reacte power compensaton requred for a common low oltage enaro, the drect on-lne startng of an nducton motor. An uncontrolled startng of an nducton motor draws sx to seen tmes the rated current, resultng n an unaeptable oltage sag n the AC power system. Voltage sags contrbute to the malfunctonng of ery senste equpment at the PCC []. Moreoer, the oltage sag durng the DOL startng of a hgh power nducton motor could be further prolonged due to an ncreased startng tme. Lengthy startng tmes are caused from a substantal reducton n the startng torque under a reduced oltage aalable at the motor termnals. The dynamc VAR deces dussed n ths paper are the Statc Compensator (STATCOM) and Statc Synchronous Seres Compensator (SSSC). The mathematcal models and control logc for the STATCOM and SSSC are deeloped and conerted to smulaton models, whch are used to demonstrate ther dynamc and steady-state performance. II. MATHEMATICAL MODEL AND CONTROL LOGIC OF THE STATCOM Fg. 1 shows the hematc for the shunt compensated nductor motor utlzng a statc compensator (STATCOM), a dynamc VAR dece. The STATCOM s desrable because t not only nstantaneously compensates reacte power at the PCC but also s capable of suppressng current harmoncs and elmnatng unbalance n the supply oltages [-5]. For STATCOM confguratons, reacte power compensaton s proded by a current-controlled oltage source nerter (CC- VSI) connected n parallel to the power system. The CC-VSI has a self-supported DC bus that allows t to supply the desred reacte power at the PCC. The swtchng deces of the acte flter are controlled usng the ndrect current control technque based on reacte power theory [6]. The actual load currents ( La,Lb,Lc ) and the PCC oltages ( pa,b,c ) are sensed and transformed nto the - frame to compute the nstantaneous alue of real (p) and reacte (q) powers consumed by the load. A. Mathematcal Model of STATCOM In Fg. 1, the hematc of the STATCOM s enclosed n the dashed box. The STATCOM crcut can be represented by the followng mathematcal equatons. dca, cb, sa, sb, = Rcca, + Lc + e (1) a, b, c where, sa,sb, are the three-phase oltages at the PCC, ca,
are the three-phase output currents from the STATCOM, and e a,b,c are the three-phase PWM oltages at the STATCOM pole ponts a, b, and c. The parameters R c and L c are the perphase STATCOM resstance and nductance, respectely. The PWM oltages at the STATCOM pole ponts are expressed n terms of the STATCOM DC bus oltage and the swtchng states (SA, SB, SC) as follows: ea = (SA -SB -SC) () eb = (-SA + SB -SC) ec = (-SA -SB + SC) On the DC sde, the current ( ) through the capactor s expressed as: d = C () where, s the oltage across the capactor. The capactor current ( ) can be expressed n terms of the nerter nput current ( c ) and current through resstor R L ( L ) as n Equaton (4). = c (4) L The current L can be expressed n terms of the DC bus oltage as n Equaton (5). L = (5) RL The nerter nput current ( c ) shown n Fg. 1 can be expressed n terms of the three output currents and the three swtchng states. The nerter nput current ( c ) s expressed as: c = ( SA) ca + (SB) cb + (SC) (6) The derate of the DC oltage can be expressed n ts fnal form usng Equatons () through (6). d (SA) = C ca (SB) + C cb (SC) + C R C The feedback-based PWM current control heme that s used to control the swtchng states (SA, SB, SC) and computaton of the releant reference currents ( ca, and ) for the close loop control of the STATCOM currents ( ca, ) s detaled n the next secton. The mathematcal smulaton and sensor-less mplementaton of a real-tme STATCOM system s carred out by solng the dfferental equatons gen n Equaton (1). Once the STATCOM currents ( ca, ) are computed, the oltages mposed across the nducton motor termnals are expressed as: dsa, sb, sa, sb, = an, bn, cn Rssa, sb, L (8) s Snce the currents ( La,Lb,Lc ) at the nput of the motor termnals are realzed through the nducton motor model, and the STATCOM currents ( ca, ) are computed aboe, the supply currents ( sa,sb, ) and ther derates can be dered n terms of these currents as n Equatons (9) and (1). = (9) sa, sb, La, Lb, Lc ca, d, L (7) dla, Lb, Lc dca, cb = (1) sa sb,, Consequently, the oltages mposed across the nducton motor termnals are computed by substtutng Equatons (9) and (1) nto Equaton (8). dla, Lb, Lc dca, = R ( ) L (11) sa sb an bn cn s La Lb Lc ca cb s B. Control Scheme of STATCOM Pror to startng the motor, the DC bus capactor s charged to obtan a desred oltage leel across the nerter s DC bus. an,bn,cn R S R S L S L S sa sb sb sa La Lb R S L S Lc HP cage rotor nducton motor LC R C c cb ca L e a C R L e b e c STATCOM Fg. 1. Schematc of shunt compensated nducton motor.
A PID controller s used to charge the DC bus capactor and contnues to montor the oltage leel of the nerter s DC bus n order to mantan the desred oltage requred to aod loss of current control and ourrence of current dstorton. The nducton motor currents ( La,Lb,Lc ) and nerter currents ( ca, ) are sensed, and the supply currents ( sa,sb, ) are computed by subtractng the nerter currents from the motor currents. The oltages mposed across the nducton motor termnals ( sa,sb, ) are computed usng the mathematcal deratons derbed n the aboe secton. The motor currents, supply currents, and motor termnal oltages are transformed nto the - reference frame to compute the nstantaneous alue of the real (p) and reacte (q) powers consumed by the motor and suppled by the source. Ths computaton s gen n Equaton (1). psply = s + s qsply = s + s (1) pmotor = s + s qmotor = s + s The reacte power consumed by the motor should come partally from the STATCOM and partally from the supply system. Howeer, to elmnate oltage sag at the PCC, t s preferred that the majorty of the reacte power comes from the STATCOM. A PI controlled s used to control the reacte power output of the STATCOM. The requred reacte power output ( q ) s calculated from the dfference between the motor sde reacte power demand and the supply sde reacte power. As shown n Equaton (1), the STATCOM reference currents n the - frame ( ) c, are computed c usng the requred reacte power output ( q ) needed to be suppled by the STATCOM [6]. s c = q s + s (1) c = s s + s The three-phase abc reference currents are obtaned by the followng expresson: 1 ca cb = 1 1 q c c (14) The reference ( ) and actual ( ca, ) nerter currents ca, are compared n a PWM current controller to generate the swtchng sgnals for the STATCOM dece. Ths control technque results n a self-supportng DC bus of the STATCOM to feed the desred reacte power at the PCC. III. MATHEMATICAL MODEL AND CONTROL LOGIC OF THE SSSC Fg. shows the hematc for the seres compensated nductor motor utlzng a statc synchronous seres compensator (SSSC), a dynamc VAR dece [7]. Contrary to the STATCOM, the SSSC s operated n oltage control mode, and therefore, a oltage-controlled oltage source nerter (VC-VSI) s used as the SSSC hardware. The SSSC njects three-phase oltages n seres wth the lne connectng the nducton motor wth the supply system. For the SSSC, an energy storage dece s used on the DC bus of the nerter to produce the desred (phase and magntude) output oltages. The njected oltages are precsely controlled to allow full compensaton at startup and only a needed compensaton afterwards. The njected oltages compensate oltage sag resultng n a ncreased startup aeleraton and substantally reduced startng tme. A. Mathematcal Model of SSSC Smlar to the mathematcal model of the STATCOM, the equatons for the three-phase SSSC currents are obtaned usng the nerter crcut shown n the dashed box n Fg. 1. The SSSC crcut can be represented by followng mathematcal equatons. dca, ea, b, c = ( Rc + Rt ) ca, + ( Lc + Lt ) (15) where, R t =R ts +R tp s the njecton transformer wndngs resstance and L t =L ts +L tp s the njecton transformer wndngs leakage nductance. The quanttes (e a,b,c ) are the nerter (SSSC power conerter) pole oltages, whch are computed as per Equaton (). The three-phase output currents of the SSSC are obtaned by solng the dfferental equatons n Equaton (15). Consequently, the three-phase oltages mposed across the nducton motor termnals (Fg. ) are computed from the three-phase SSSC output currents. As shown n Equaton (16), for seres compensaton, the njected oltage ectors produced by the SSSC are added wth the supply oltage ectors, resultng n compensaton of the desred reacte power. a_nj,b_nj,c_nj Three-phase AC Mans an, bn,cn L s R s Injecton Transformer s as,bs,cs a b sa,sb, L Energy Storage Dece VC-VSI HP cage rotor nducton motor Fg.. Sngle lne dagram of an acte seres compensated nducton motor.
4 dsa, sb, sa, sb, = anbn cn Rs sa, sb, Ls + (16) a, b, c_ nj The njected oltages ( a-nj,b-nj,c-nj ) mposed on the njecton transformer prmary (Fg. ) are realzed by the oltage control of the SSSC power crcut. The mathematcal relatonshp between the njected oltages and nerter currents are gen n Equaton (17). dca, = ( R + R ) + ( L + L (17) a, b, c _ nj ts tp ca, ts tp) The heme used to control the swtchng states (SA, SB, SC) and njected oltages s derbed the next secton. B. Control Scheme of SSSC Unlke shunt compensaton, the SSSC system requres a constant DC bus oltage, whch s ensured by usng a 15V DC supply to feed power to SSSC DC bus. The nducton motor currents ( La,Lb,Lc ) are sensed, and the oltages appearng at both sdes (( as,bs,cs ) and ( sa,sb, )) of the njecton transformer are computed to determne the real (p) and reacte (q) powers consumed by the motor and fed by the supply system. The dfference between the reacte power consumed by the motor and suppled by the source s produce by the SSSC. The nstantaneous alue of real (p) and reacte (q) powers consumed by the motor and suppled by the source are expressed n Equaton (18). psply = s + s qsply = s + s (18) pmotor = s + s qmotor = s + s To elmnate oltage sag at the PCC, t s preferred that the majorty of the reacte power consumed by the motor be produced by the SSSC a a PI controller based heme. The requred reacte power (q) s obtaned from the dfference between the motor sde reacte power demand and the supply sde reacte power output. Shown n Equaton (19), the SSSC reference oltages n - frame ( _ nj, _ nj ) are computed usng the desred alue of reacte power that s to be suppled from the SSSC. 1 _ nj L L p = = (19) _ nj L L q In Equaton (19), settng the real power (p) equal to zero ensures that the SSSC feeds only reacte power and requres the mnmal amount of energy storage on ts DC bus. For oltage control, the - frame ( _ nj, _ nj ) reference oltages are transformed nto the abc reference frame usng mathematcal expressons smlar to those n Equaton (14). After beng transformed nto the abc reference frame, these reference oltages are compared wth the actual njected oltages (oltages across njecton transformer, see Equaton 17). The obtaned dfference oltage sgnals are compared wth a trangular waeform control sgnal. Comparson of the dfference oltage sgnals wth the trangular waeform results n swtchng sgnals for the SSSC deces. The swtchng sgnals ensure that actual njected oltages follow the reference njected oltages. IV. PERFORMANCE OF DYNAMIC VAR DEVICES The deeloped mathematcal models of the STATCOM, SSSC, and control algorthms are used to assess the performance and effecteness of the dynamc VAR compensaton hemes. The models are deeloped n C, and the smulated results for a HP motor are gen below. A. Results for an Inducton Motor wthout VAR Compensaton A 6 Hz, HP nducton motor s smulated wth the followng parameters: RS =.511Ω RR =.489Ω LS =.49H LR =.49H The three-phase oltage supply has a peak ampltude of 587. V. The nerta of the load s set to be.7 kg-m. Fg. (a) shows the startng speed of the nducton motor. Wthout compensaton, the motor needs approxmately.89 seconds to start. Fg (b) shows the phase a oltage appearng at the motor termnal. A sgnfcant amount of oltage sag s obsered untl the motor has fully started. Fg. 4 shows the phase a lne current when the motor s started. A large current nrush s present whch s capable of dsturbng the supply system. 4 1 8 6 4 - -4-6 -8 (a) (b) Fg.. Startng response of hgh power nducton motor wthout any compensaton (a) speed of the nducton motor and (b) phase a oltage sa across the motor wndng.
5 Current (A) 5 1-1 - -5 Fg. 4. Startng current for the phase a wndng ( La ) of a hgh power nducton motor wthout any compensaton. B. Results for an Inducton Motor wth Shunt Compensaton The results for the shunt compensated system for the nducton motor are shown below. Fg. 5(a) shows the startng speed of the shunt compensated nducton motor. The motor s started at.1 seconds (ths tme s needed to charge STATCOM DC bus) and reaches the fnal speed at.76 seconds. Wth ths heme, the motor needs approxmately.66 seconds to start and consequently, starts up faster than the system wthout compensaton. Fg. 5(b) shows the phase a oltage appearng at the motor termnal. The duraton of the oltage sag s reduced and causes the startup aeleraton of the nducton motor to ncrease. Fg. 6 shows the phase a lne current when the motor s started. The hgher startng current produces a hgher startng torque whch consequently reduces the motor startng tme. 4 1 8 6 4 - -4-6 -8 (a) (b) Fg. 5. Startng response of a hgh power nducton motor wth a STATCOMbased compensaton technque (a) speed of the nducton motor and (b) phase a oltage sa across the motor wndng. 5 4 1-1 - - -4-5 Fg. 6. Startng current for the phase a wndng ( La ) of a hgh power nducton motor wth the STATCOM-based compensaton technque. Current (A) C. Results for an Inducton Motor wth Seres Compensaton The results for the seres compensated system for the nducton motor are shown below. Fg. 7(a) shows the startng speed of the seres compensated nducton motor. Wth ths heme, the motor needs approxmately.56 seconds to start and consequently starts up faster than the shunt compensated system. Fg. 7(b) shows the phase a oltage appearng at the motor. The duraton of the oltage sag s reduced, whch rases the alue of motor startup aeleraton. Also, the amount of oltage sag s decreased from V (wthout compensaton) to 1 V wth the seres compensated system. Ths reducton n magntude also contrbutes to reducton n the motor startup tme. Fg. 8 shows the phase a lne current when the motor s started. The hgher startng current produces a hgher startng torque, whch consequently reduces the startng motor tme. 4 1 8 6 4 - -4-6 -8 (a) (b) Fg. 7. Startng response of a hgh power nducton motor wth the SSSCbased compensaton technque (a) speed of the nducton motor and (b) phase a oltage sa across the motor wndng.
6 Current (A) 5 1-1 - -5 Fg. 8. Startng current for the phase a wndng ( La ) of a hgh power nducton motor wth SSSC-based compensaton technque. Fg. 9 shows the njected oltage, whch s added wth the PCC supply, thereby rasng the oltage mposed across the motor wndngs. Wth the VC-VSI based seres compensaton heme, the njected oltage drops to a sgnfcantly low alue as soon as motor starts and reaches ts fnal speed. Therefore, as compared to seres swtched capactor systems, seres compensaton not only offers superor performance but also results n a relable and mantenance free operaton. VI. REFERENCES [1] FERC Staff Report, Prncples for effcent and relable reacte power supply and consumpton, Feb. 5. [] A. Bendre, D. Dan, W. Kranz, and W. E. Brumsckle, Are oltage sags destroyng equpment?, IEEE Industry Applcatons Magazne, ol. 1, no. 4, pp. 1-1, Jul./Aug. 6. [] B.-S. Chen and Y.-Y. Hsu, A mnmal harmonc controller for a STATCOM, IEEE Trans. Industral Electroncs, ol. 5, pp. 655-664, Feb. 8. [4] K. L, J. Lu, Z. Wang, and B. We, Strateges and operatng pont optmzaton of STATCOM control for oltage unbalance mtgaton n three-phase three-wre systems, IEEE Trans. Power Delery, ol., no. 1, pp. 41-4, Jan. 7. [5] S.-J. Tsa and Y. Chang, Dynamc and unbalance oltage compensaton usng STATCOM, n Proc. IEEE Power and Energy Socety General Meetng, Jul. 8. [6] B. N. Sngh, B. Sngh, A. Chandra, P. Rastgoufard, and K. Al-Haddad, An mproed control algorthm for acte flters, IEEE Trans. Power Delery, ol., no., pp. 19-1, Apr. 7. [7] P. Zunga-Haro and J. M. Ramrez, Multpulse VSC based SSSC, n Proc. IEEE Power and Energy Socety General Meetng, Jul. 8. 5 1-1 - -5 Fg. 9. Injected oltage n seres wth the motor. V. CONCLUSION Two noel dynamc shunt and seres compensaton hemes for motor startng are presented n ths paper. Instantaneous reacte power theory s utlzed to obtan an mproed control algorthm for the oltage source nerter operatng n current control mode for shunt compensaton and n oltage control mode for seres compensaton. Mathematcal models for both compensaton hemes are dered and coded n C to obtan smulaton results. The smulated results reeal that the proposed compensaton technques are found to be effecte as they mnmze the problem of oltage sag and current nrush. It s obsered that the compensaton technques result n a substantal rse n the startup aeleraton whle reducng the oerall startup tme of the hgh power nducton motor.