Fractional order PI based STATCOM and UPFC controller to diminish subsynchronous resonance

Transcription

1 DOI /s y RESEARCH Open Access Fractonal order PI based STATCOM and UPFC controller to dmnsh synchronous resonance D. Koteswara Raju 1*, Bhmrao S. Umre 1, Anjal S. Junghare 1, Mohan P. Thakre 1, Rambabu Motamarr 1 and Chatanya Somu 2 *Correspondence: eswaar.raju@gmal.com 1 Department of Electrcal Engneerng, VNIT, Nagpur, Maharashtra, Inda Full lst of author nformaton s avalable at the end of the artcle Abstract Ths research artcle proposes a powerful fractonal-order PI controller to mtgate the synchronous oscllatons n turbne-generator shaft due to synchronous resonance (SSR) wth flexble AC transmsson system devces such as statc synchronous compensator (STATCOM) and unfed power flow controller (UPFC). The dmnuton of SSR s acheved by the rasng of network dampng at those frequences whch are proxmate to the torsonal mode frequency of the turbne-generator shaft. The ncrease of network dampng s obtaned wth the njecton of synchronous frequency component of current and both current and voltage nto the lne. The synchronous component of current and voltage are derved from the measured sgnal of the system and further the same amount of shunt current s njected wth STATCOM and smultaneous njecton of current and voltage wth UPFC nto the transmsson lne to make the synchronous current to zero whch s the prme source of turbne shaft oscllatons. The nserton and proper tunng of Fractonal-order PI controller n the control scheme, the synchronous oscllatons are reduced to 92 % n case of STATCOM and 98 % n case of UPFC as compared to wthout controller and 14 % as compared wth the results of conventonal PI controller. The IEEE frst benchmark model has adopted for analyze the effectveness and speed of the proposed control scheme usng MAT- LAB-Smulnk and the correspondng results llustrates the precson and robustness of the proposed controller. Keywords: Fractonal-order PI controller, STATCOM, Torque amplfcaton, Voltage source converter, UPFC Background Seres capactor compensaton has been broadly employed n Power system to cancel a porton of reactance of the lne mpedance to ncrement the power transfer capablty of long hgh voltage (HV) and extra hgh voltage (EHV) transmsson lnes further load sharng among parallel lnes and boosts the steady state and transent stablty lmts (Anderson et al. 1989; IEEE SSR Workng Group 1985). However, the addton of capactve compensaton n seres can cause a new dffculty of turbne-generator shaft oscllatons wth below the system frequency due to Subsynchronous Resonance (SSR). The synchronous oscllatons can be excted durng the fault or dsturbance n the 2016 The Author(s). Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton 4.0 Internatonal Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made.

2 Page 2 of 20 transmsson lne wth seres capactors, when the normal system frequency matches wth the complement of any of the mode frequency of the shaft system (Kundur 1994; Padyar 1998). Latest advancement of power electronc devces led to the mprovement of FACTS devces such as thyrstor controlled seres capactor (TCSC), statc synchronous compensator (STATCOM), statc synchronous seres compensator (SSSC) and unfed power flow controller (UPFC) (Hngoran and Gyugy 2000). An astronomcally mmense number of methods and solutons have been addressed by the dfferent researchers to avod the problem of SSR wth the concern of FACTS devces (Padyar and Swayam Prakash 2003; Padyar and Prabhu 2006; Bongorno et al. 2008b, c; Mohan et al. 2015; Koteswara Raju et al. 2016). The selecton of controller s depends on extracton of the synchronous frequency components wth hgh speed and accuracy. From the knowledge of synchronous frequency component of current and voltage a proper protecton system s desgned to avod shaft breakage due to SSR (Bongorno et al. 2008a). The mtgaton of SSR by the njecton of shunt current wth STATCOM ncludng proportonal ntegrator controller (PI) s proposed n reference (Umre et al. 2007). The STATCOM wth synchronous dampng controller (SSDC) ncludng type 1 and type 2 controller s proposed based on the tunng of parameters usng dampng torque method to mtgate the SSR (Padyar and Swayam Prakash 2003; Padyar and Prabhu 2006). The parameters of SSDC are tuned to get good performance to provde dampng (postve) n the range of torsonal mode frequences. The dampng of SSR oscllatons wth 48 pulses (three-level) VSC based STATCOM usng remote sgnal s proposed n (Salemna et al. 2008). The problem of SSR can also be bypassed by a proper combnaton of hybrd seres compensaton conssts of FACTS controllers (SSSC) along wth passve components. The mtgaton of SSR wth the proper njecton of seres voltage usng PI based SSSC s descrbed n (Bongorno et al. 2008b, c; Mohan et al. 2015). The njecton of synchronous frequency component of voltage n seres wth synchronous current suppresser usng SSSC based on the knowledge of synchronous current to damp out the SSR s proposed n (Panda et al. 2010, 2016;Thrumalavasan et al. 2013). In ths paper a Fractonal-order proportonal ntegrator (FOPI) based STATCOM and UPFC s used for mtgatng the synchronous oscllatons n turbne-generator shaft due to SSR. The mtgaton of SSR s done by the njecton of shunt current by STAT- COM and the smultaneous njecton of voltage and current nto the lne by UPFC wth reference to the synchronous components whch are extracted from the lne. The STATCOM and UPFC are constructed wth the help of mult-pulse voltage source converters. The fractonal-order P I λ D µ controller derved from conventonal PID controller wth ntegrator of real order λ and dfferentator of real order µ. Takng λ = 1 and µ = 1, we obtan a classcal PID controller. If µ = 0 and K d = 0, we obtan a P I λ controller, etc. All these types of controllers are partcular cases of the P I λ D µ controller, whch s more flexble and gves the adjustment of dynamcal propertes of the fractonal-order control system. In P I λ D µ controller there are fve parameters to tune, wth respect to the three parameters of the standard PID controller (λ and µ are equal to one) (Igor Podlubny 1999; Shantanu Das 2008). The faclty of fne tunng of Fractonal-order PI n the control crcut of STATCOM and UPFC controllers the synchronous oscllatons are

3 Page 3 of 20 reduced to 92 and 98 % as compared to wthout controller and 14 % as compared to conventonal PI controller. Fractonal-order PI controllers havng larger stablty lmt wth larger phase value as compared to PI controller. Moreover, the Fractonal-order PI controllers (FOPI) exhbts a less negatve phase than the PI controller and t mples that more robustness (n the sense of stablty) to changes n the overall system parameters. The paper s organzed n four sectons. Study system (IEEE FBM) wth UPFC controller secton descrbes UPFC connected IEEE frst benchmark model (study system) and the procedure for realzaton of synchronous frequency component of current and voltage. The desgn of synchronous frequency component controller ncludng PI and Fractonal-order PI controller and further the study system parameters and specfcatons of FACTS devces are presented n Subsynchronous frequency component controller secton. The FFT analyss of LPB-GEN torque sgnal and smulaton results of IEEE frst benchmark model wthout and wth FACTS controller under symmetrcal (L L-L) fault usng PI and Fractonal-order PI controller s gven n Results and dscussons secton. The Concluson secton represents the concluson of the complete research work. Study system (IEEE FBM) wth FACTS controller The block dagram of study system (IEEE FBM) wth FACTS controller s shown n Fg. 1. The one lne dagram of study system wth STATCOM s smlar as shown n Fg. 1 and only dfference s that the STATCOM s connected n shunt to the lne. The generated voltage and the grd current are expressed as v s and respectvely. The njected current and voltage by seres and shunt converters are denoted as v SSSC and STAT. The man prncple of SSR mtgaton wth classcal control scheme s to restore the voltage generated of frequency of fundamental by the added bank of fxed capactor by njectng a voltage of lke magntude wth seres converter (Bongorno et al. 2008b, c; Koteswara Raju et al. 2016). Wth the njecton of shunt current by STATCOM and both current and voltage nto the lne by UPFC elmnates the capactve reactance of the capactor bank and further shfts the system resonance (electrcal), thus avods the problem of synchronous resonance. Several publcatons have descrbed the capablty of used control method (Bongorno et al. 2008b, c; Thrumalavasan et al. 2013; Mohan et al. 2015; Panda et al. 2010, 2016; Koteswara Raju et al. 2016). The analytcal procedure for Generator G V S X T R L X L X C X SYS V g I STAT V SSSC Infnte bus UPFC Shunt Seres G LPB LPA IP HP Fg. 1 Study system model (IEEE FBM) ncludng UPFC controller Turbnes

4 Page 4 of 20 realzaton of current and voltage components of synchronous frequency from the sgnal whch s measured from the transmsson lne s proposed as fallows. Realzaton of current and voltage components of synchronous frequency The current and voltage components of below synchronous frequency at the generator termnals are realzed by consderng the generc case of a transmsson lne connected wth synchronous generator. The generator voltage n terms of α and β-plane s wrtten as v () s = v s,α (t) + jv s,β (t) = ω(t)v s e j(ω 0t+δ(t)) (1) where V s s the magntude of termnal voltage of generator at rated speed, phase dsplacement s gven by δ, ω(t) s the speed of rotor n per-unt and ω 0 s the fundamental angular frequency radans/second. The speed of the generator rotor n terms of fundamental angular frequency ω 0, and oscllatng angular frequency ω m s gven by ω(t) = ω 0 + A sn (ω m t) (2) where A denotes the oscllaton magntude and ω m s the frequency of rotor oscllatons. By applyng dervatve to the rotor angle d dt δ(t) = [ω(t) ω 0]ω B = A sn (ω m t)ω B (3) where, ω B s the rated frequency n radans/sec. To get δ 0.e. the steady state rotor angle, ntegrate Eq. (3) on both sdes. The angle of rotor s expressed as δ(t) = δ 0 A ω B ω m cos (ω m t) (4) When the system jected to SSR, a small dsturbance to generator rotor produces the voltage and current conssts of three components: fundamental frequency, bellow synchronous frequency and above synchronous frequency. A lttle dampng of postve s offered by network for super-synchronous frequency; hence the rsk offered to generatng staton by ths less (Bongorno et al. 2008b). The voltage of synchronous frequency component n α and β-plane s gven by v s, (t) = AV s 2ω m (ω 0 ω m )e j[(ω 0 ω m )t+δ 0 + π 2 ] (5) Transformed vector of grd voltage n d-q plane s gven by v s (t) = v () s (t)e jω0t = v () s,f (t) + v () s, (t) (6) where v () s,f s the fundamental frequency and the -synchronous frequency component n d-q plane s wrtten as v () s, (t) = v() s, (t)e jω 0t = AV s 2ω m (ω 0 ω m )e j[ω mt+δ 0 + π 2 ] (7)

5 Page 5 of 20 The termnal voltage n terms of co-ordnate system wth a small dsturbance s gven by v s (t) = v (t) + v() (t) + v() s,f s, s,sup(t) (8) Fgure 2 represents the block dagram of Low Pass Flter (LPF) based estmaton of synchronous components. f sup and f represents the super-synchronous and synchronous frequency component. Consder the generator rotor oscllates wth angular frequency ω m and the Eq. (7) can be rewrtten n m -plane as v s (t) = v s,f (t) + m) v( (t)e jω mt s, (9) The rearrangement of Eq. (8) gves the extract of -synchronous frequency component, so that v s,f and v() s, become solated and gven to flter (Low pass). The output of Estmaton of synchronous component (ESSC) s [ ] v s,f (t) = H f(p) v s (t) v s, (t)ej(ω mt) [ ],f (t) = H f (p) (t) (t)ej(ω mt) [ ] v m s, (t) = H (p) v s (t)e j(ωmt) v s,f (t) e j(ω mt) (10) (11) (12) [ ] m (t) = H (p) (t)e j(ωmt) f (t) e j(ω mt) (13) v s θ f v s Low pass flter 1 Low pass flter 2 v s, v s, f j e ω m v m s, θ f Low pass flter 1 Low pass flter 2 f j e ω m m Fg. 2 Low pass flter based estmaton of synchronous components (ESSC)

6 Page 6 of 20 The transfer functons of low pass flter (LPF) are H f (p), and H (p). The synchronous frequency component of voltage s wrtten as v s, (t) = H ( ) [ ] p + jωm v s (t) v s,f (t) (14) Smlarly the synchronous frequency component of current s wrtten as s, (t) = H ( ) [ ] p + jωm s (t) s,f (t) (15) The voltage component of synchronous and fundamental frequency s obtaned by combnng Eqs. (10) and (14). Equatons (11) and (15) are used for the estmaton of current component of synchronous and fundamental frequency. Subsynchronous frequency component controller To make the current component of synchronous to zero, the ntatve of the proposed scheme s to generate and nject the nternal bus current of synchronous wth STATCOM and current, voltage by UPFC. The Laplace doman of the -synchronous component current controller (SSCC) can be expressed as V ( m) SSSC (s) = v m g, (s) + ( R + j(ω ω m ) ( L T + L )) ( m) (s) ( + K p + K ) [ ] ( m) s (s) ( m) (s) I ( m) STAT (s) = m s, (s) + v ( m) g, ( (s) R + j(ω ωm ) ( L T + L )) [ ( ) + v ( m) /( g, (s) v( m) g, (s) K p + K )] s (16) (17) where R, L and L T are the upstream system resstance wth FACTS devce, the generator transent nductance and transformer leakage nductance respectvely. ( m) s the current reference, K and K p are the ntegral and proportonal gans of the PI-controller. Fractonal order PI (FOPI) controller The fractonal-order P I λ D µ controller was proposed as a generalzaton of the PID controller wth ntegrator of real order λ and dfferentator of real order µ. The transfer functon of such type of controller n Laplace doman has form (Igor Podlubny 1999; Shantanu Das 2008): C(s) = U(s) E(s) = K p + K s λ + K d s µ, (λ µ > 0) (18) where K p s the proportonal constant, K s the ntegraton constant and K d s the dfferentaton constant. Transfer functon (18) corresponds n dscrete doman wth the dscrete transfer functon n the followng expresson (Cao and Cao 2006; Enrco Pson et al. 2009):

7 Page 7 of 20 ( C z 1) = U( z 1) ( E ( z 1) = K p + K ω (z 1)) λ ( ( + Kd ω z 1)) µ, (λ, µ > 0) (19) where λ and µ are arbtrary real numbers. To get P I λ controller sttute µ = 0 and K d = 0. Wth the use of Fractonal-order PI controller the Eq. (19) and (20) can be wrtten as V ( m) SSSC (s) = v m g, (s) + ( R + j(ω ω m ) ( L T + L )) ( m) (s) ( ) [ + K p + Kλ ] ( m) s (s) ( m) (s) I ( m) STAT (s) = m s, (s) + v ( m) g, ( (s) R + j(ω ωm ) ( L T + L )) [ ( ) v ( m) /( )] g, (s) v( m) g, (s) K p + Kλ s (20) (21) The Fractonal-order PI controller provdes the faclty for fne tunng of controller to acheve better result as compare to conventonal PI controller. Wth the faclty of choosng the approprate K p, K and λ values, the fne tunng of controller reduces the SSR oscllatons wth a faster rate. The complete block dagram of synchronous frequency component controller s shown n Fg. 3. At Frst the current and voltage of three-phase are measured from transmsson lne and further converted nto plane, wth the help of θ f (transformaton angle) agan converts nto to -coordnate system. The outcome of estmaton unt s the synchronous and fundamental frequency component of current and voltage n -frame. The synchronous frequency component n -reference s converted nto synchronous frequency m -frame wth the help of θ m (transform angle) whch s obtaned by ntegratng ω m (oscllatng frequency). The consequental sgnals are gven to the synchronous frequency component controller (SSCC). The output of Subsynchronous component controller s agan transferred nto and further transferred to abc and are furthermore gven to the Pulse wdth modulaton (PWM) generator whch ssues frng sgnals to 3-phase 48 pulse (three-level) GTO based voltage source converters (VSC). v abc g abc abc abc v g PLL θ f θ f ω f v g Estmaton of Subsynchronous Component v g, θ m m m m v g, m Subsynchronous component controller v m sssc m m sssc θf θ m Fg. 3 Schematc dagram of the synchronous frequency component controller m θf θ m v sssc sssc PWM Generator

8 Page 8 of 20 Parameters and specfcatons of IEEE frst benchmark model To nvestgate the capablty of the proposed control scheme the well-known IEEE FBM wth fve mass systems has consdered and the parameters of the system are shown n Tables 1, 2 and 3. The turbne-generator set of ratng MVA connected through radal compensated (seres) lne to an nfnte bus and the correspondng voltage s 539 kv of 60 Hz frequency. A Matlab code s developed to outlne the natural frequences of turbne and mode shapes (Anderson et al. 1989; Kundur 1994). The natural frequences are , , , , and Hz. For 55 % seres compensaton the resonant frequency s Hz (Kundur 1994). The selecton of tuned values for the parameters of PI controller s gven n (Bongorno et al. 2008c) and the FOPI controllers are gven n Table 4. Ratng of shunt and seres converters of UPFC A three-phase 48 pulse (three-level) VSC brdge s used for Shunt and Seres Converters. The VSC characterzed n ths research work s a harmonc neutralzed 48-pulse GTO based nverter. These arrangements are made to produce harmonc free voltage Table 1 IEEE Frst benchmark network parameters Resstance of network R L per unt Reactance of transformer X T per unt Transformaton rato 22 kv/539 kv Reactance of lne X L 0.50 per unt Reactance of transmsson lne X sys per unt Table 2 Synchronous machne parameters Parameter Value (per unt) Tme constant Value (sec) X a T d0 X d 1.79 T d X d X d T q T q X q 1.71 X q X q Table 3 IEEE frst benchmark shaft parameters Inerta H [ s 1] Shaft secton Sprng constant [per unt T/rad] Hgh pressure turbne HP-IP Intermedate pressure turbne IP-LPA Low pressure A turbne LPA-LPB Low pressure B turbne LPB-GEN Generator

9 Page 9 of 20 Table 4 Parameters of PI and FOPI controllers Controllers K p K λ PI FOPI Fg. 4 The FFT analyss of rotor speed and LPB-Gen Torque sgnal wthout controller. a Determnaton of domnant mode wth FFT analyss on rotor speed sgnal of generator and b FFT analyss on LPB-Gen Torque sgnal wthout controller output by proper connectng 6-pulse VSC s. 12-pulse confguraton s acheved by connectng two 6-pulse VSC s, two 12-pluse converter are used for a 24-pulse topology and two 24-pulse arrangements are used for obtan a 48-pulse VSC. To produce a 48-pulse waveform wth a harmonc content of n = 48 m ± 1, where m = 0, 1, 2,, the 6-pulse converters requres relatve phase dsplacements accomplshed va the gate pulse pattern

10 Page 10 of 20 that determnes the angle of the resultng three phase output voltages. Also, PST s are used and are connected n serally wth the phase voltages n the prmary sde of the MCC transformers to add voltage components n quadrature. These quadrature voltages are obtaned from the three phase output voltages of each VSC (Kumar and Ghosh 1999; Hngoran and Gyugy 2000; Salemna et al. 2008). The ratng of power necessary to dmnsh the SSR s dffcult to conclude and depends on level of compensaton (seres), duraton and locaton of fault. As the amount of current and voltage components of synchronous frequency s reduced, the Shunt and Seres converter ratng s also reduced (0.1 5 %). The power ratng s 12 MVA and the voltage ratng s 8 kv (ether capactor or Drect current source). For an actve power of 0.5 pu, the results are obtaned and analyzed n the paper. Results and dscussons FFT analyss To assess the oscllatory modes of IEEE Frst Benchmark model, Fast Fourer Transform (FFT) analyss has been made on rotor speed and the correspondng response s shown n Fg. 4a. Wth 55 % seres compensaton the electrcal resonance frequency concdes wth mode 2 of the IEEE FBM, for ths the system s unstable. By observng Fg. 4a, there are three modes are present n whch mode 2 ( Hz) s more domnant than other two. The torque amplfcaton effect between LPB and Generator for a tme nterval from 0 to 10 s wth dvson of 3 s n order to clearly observe the domnant mode of SSR and the correspondng results of FFT based analyss wthout controller s shown n Fg. 4b. The domnant mode (Mode-2) component ncreases wth tme as shown n Fg. 4b. Hence there s a requrement of controller to mtgate ths adverse, oscllatory and ncreasng component of nstablty n the rotor shaft so as to protect the power system from damage. Fgure 5 shows the FFT analyss of LPB and Generator torque sgnal wth controller. Fg. 5 FFT analyss on LPB-Gen Torque sgnal wth controller

11 Page 11 of 20 The synchronous mode wth frequency of 24.8 Hz s reduced (mtgated) wth the addton of controller and a small value s at Hz whch s not harm to the system s shown n Fg. 5. Stress analyss Transent dsturbance n the generator produces acceleratng torque (T a ). Due to ths torque, varyng stress s produces n the rotor shaft. When ths stresses exceeds the endurance lmt.e N/m 2, the shaft wll be damaged. The torsonal fatgue of turbne generator shaft s prmarly as a functon of ampltude of the stress and secondarly on ts lmt (Kundur 1994). The calculaton of mechancal stress needs the calculaton of mechancal angle (twst angle between shafts) δ and s as fallows. [M] [ δ ] + [ D ][ δ ] + [K][δ] = [T m ] [T e ] (22) Fg. 6 Smulated Torque and Stress between LPB-Generator of IEEE frst benchmark model wthout controller and wth PI based STATCOM controller. a Wthout controller and b Wth PI based STATCOM controller

12 Page 12 of 20 where, [M] s dagonal matrx, consstng of nerta of all masses, [ D ] s tr dagonal symmetrc matrx consstng of, varous dampng coeffcents of the masses, [K] s tr dagonal symmetrc matrx consstng of torsonal stffness of varous mass sectons, [T m ] conssts of mechancal torque actng on varous masses, [T e ] conssts of electrcal torque produced by varous masses. The mechancal stress or Fatgue between any shaft systems s gven as F = {(δ δ +1 ) G R}/L (where = 1to5) (23) where F: Fatgue or Mechancal stress n N/m 2, δ, δ +1 : twst angle of th mass to the ( + 1)th mass n radans, G: modulus of rgdty n N/m 2 ; L: length of shaft n meters; R: radus of shaft n meters. Fg. 7 Smulated Torque and Stress between LPB-Generator of IEEE frst benchmark model wth FOPI based STATCOM and PI based UPFC controllers. a Wth FOPI based STATCOM controller and b Wth PI based UPFC controller

13 Page 13 of 20 Smulaton results To realze the performance of the suggested control scheme to dmnsh the SSR due to Torque Amplfcaton, the IEEE FBM wth STATCOM and UPFC has been smulated usng Matlab-Smulnk software. A three-phase fault s appled to the grd at 1 s for tme duraton of 0.05 s wth 55 % seres compensaton. The smulaton results are shown for three cases, wthout controller, wth PI and wth FOPI based STATCOM and UPFC controller. After the clearance of fault at 1.05 s the system has to regan ts prevous state that s the turbne-generator shaft oscllatons are at normal level. Under synchronous resonance condton the system s very senstve, further a small fault or dsturbance causes large amplfcaton of turbne-generator oscllatons and furthermore ncreases the stress and twst between the shaft sectons that wll damage the entre system. Fgures 6, 7 and 8 show the smulated Torque and Stress between LPB-Generator shaft wthout controller and wth STATCOM and UPFC controller. Due to the unstable mode, when the fault s cleared, large oscllatons wll be experenced between the dfferent sectons of the turbne-generator shaft. Fgure 6a shows the torque and stress between LPB and Generator wthout controller. For the sake of smplcty the torque and stress between remanng shaft systems experence the same and are not shown. The torque and stress ncreases wth a fast rate after fault clearance whch wll damage the turbne shaft system. The torque between LPB and Generator ncreases to 75 tmes and the stress ncreases to N/m 2 whch wll damage the entre shaft system. To avod the damage due to torque amplfcaton effect of SSR the PI controller based STATCOM or UPFC s connected to the lne. The PI based STATCOM njects a shunt current or smultaneous njecton of shunt current and seres voltage wth UPFC nto the lne n order to reduce the capactve reactance from the capactor bank and further shft the electrcal resonance of the system, thus avodng the rsk of SSR. The smultaneous njecton of shunt current and seres voltage wth UPFC, the turbne oscllatons and stress are reduced to such a low value about 94 % as compared to wthout controller. Wth PI based STATCOM controller the torque between LPB and Generator Fg. 8 Smulated Torque and Stress between LPB-Generator of IEEE frst benchmark model wth FOPI based UPFC controller. Wth FOPI based UPFC controller

14 Page 14 of 20 s reduced from 2.2 to 0.3 pu and further reduced from 0.46 to 0.09 pu n case of UPFC. Smlarly the Mechancal stress between LPB and Generator s reduced from to N/m 2 wth STATCOM and 0.45 to N/m 2 wth UPFC for a tme nterval of 10 s shown n Fgs. 6b and 7b. Wth the faclty of fractonal tunng of FOPI controller the torque between LPB and Generator s further reduced from 2.1 to 0.28 pu n case of STATCOM and from 0.42 to 0.08 pu wth UPFC. Smlarly the Mechancal stress s furthermore reduced from to N/m 2 n case of STATCOM and from to N/m 2 n case of UPFC for a tme nterval of 10 s shown n Fgs. 7a and 8. Fgures 9, 10 and 11 show the change n Electromagnetc torque and Rotor speed wthout and wth controllers. Wthout controller both are ncreasng drastcally wll lead to shaft damage of Turbne-Generator set shown n Fg. 9a. The Electromagnetc torque ncreases Fg. 9 Change n Electro-Magnetc torque and change n Rotor speed of IEEE frst benchmark model wthout controller and wth PI based STATCOM controller. a Wthout controller and b Wth PI based STATCOM controller

15 Page 15 of 20 Fg. 10 Change n Electro-Magnetc torque and change n Rotor speed of IEEE frst benchmark model wth FOPI based STATCOM and PI based UPFC controllers. a Wth FOPI based STATCOM controller and b Wth PI based UPFC controller Fg. 11 Change n Electro-Magnetc torque and change n Rotor speed of IEEE frst benchmark model wth FOPI based UPFC controller. Wth FOPI based UPFC controller

16 Page 16 of 20 to 1.8 tmes and the rotor speed also ncreases to 1.28 tmes whch s beyond the tolerable lmt of Turbne-Generator Shaft system. Fgures 9b and 10b show the reducton of change n Electromagnetc torque to a safe value from 0.9 to 0.05 and 0.27 to 0.01 pu and smlarly the change n Rotor speed from to and to pu wth PI based STATCOM and UPFC controllers for a tme nterval of 10 s. Wth the use of FOPI nstead of PI controller the change n Electromagnetc torque s further reduced from 0.86 to 0.04 and 0.25 to 0.01pu and the change n Rotor speed are also reduced from to pu and to n case of STATCOM and UPFC for a tme nterval of 10 s shown n Fgs. 10a and 11. By consderng the Fgs. 9b, 10a, b and 11 the concluson s that both the controllers reduce the effect of SSR on Electromagnetc torque and Rotor speed and further the FOPI based controllers are more effectve than conventonal PI based controllers. Fgures 12 and 13 show the Current njected by STATCOM and smultaneous njecton of current and voltage by UPFC controllers durng three-phase fault to mtgate the Fg. 12 Injected currents of PI and FOPI based STATCOM controllers durng three-phase fault to mtgate the SSR. a Current njected by PI based STATCOM controller and b Current njected by FOPI based STATCOM controller

17 Page 17 of 20 Fg. 13 Current and voltage njected by PI and FOPI based UPFC controllers durng three-phase fault to mtgate the SSR. a Shunt current and seres voltage njected by PI based UPFC controller and b Shunt current and seres voltage njected by FOPI based UPFC controller SSR wth PI and FOPI controllers. The magntude of njecton current by PI based STA- COM s 1700 A and the magntude of smultaneous njecton of current and voltage wth PI based UPFC s approxmately 600 A and 100 V durng fault perod shown n Fgs. 12a, 13a. The magntude of njected current of STATCOM s reduced to 1600 A and smultaneous njecton of current and voltages of UPFC s reduced to approxmately 550 A and 60 V durng fault perod wth FOPI based controller shown n Fgs. 12b, 13b respectvely. Due to reducton of njected current by STATCOM and smultaneous njected current and voltage by UPFC the burden on converters are further reduced. Ths s the addtonal achevement of the proposed Fractonal-order PI control scheme. Table 5 gves the comparson of varous performance ndexes of IEEE frst bench mark model wth PI and FOPI based STATCOM and UPFC. The table gves the complete dea of reducton of varous performance ndexes of IEEE frst benchmark model wth PI and FOPI based controllers for a smulaton tme nterval of 10 s.

18 Page 18 of 20 Table 5 Comparson of dfferent performance ndexes of IEEE frst benchmark model wth PI and wth FOPI based STATCOM and UPFC controllers 1. LPB-GEN Torque (per unt) Wth PI based controller the torque s reduced from 2.2 to 0.3 pu n case of STATCOM and from 0.46 to 0.09 pu wth UPFC for a tme nterval of 1.05 s to 10 s. The torque s further more reduced wth FOPI controller from 2.1 to 0.28 pu n case of STATCOM and from 0.42 to 0.08 n case of UPFC 2. LPB-GEN Stress (10 7 N/m 2 ) The Mechancal stress between LPB and Generator s reduced from to N/m 2 and 0.45 to N/m 2 wth PI based STATCOM and UPFC for a tme nterval of 1.05 to 10 s. Much more reducton of stress s obtaned wth the help of FOPI based controller from to N/m 2 and from 0.45 to N/m 2 n case of STATCOM and UPFC 3. Change n Electro-Magnetc Torque (per unt) The Electromagnetc torque s reduced and reaches to a safe value from 0.9 to 0.05 and 0.27 to 0.01 pu wth PI based STATCOM and UPFC controllers for a tme nterval of 1.05 to 10 s. Wth the use of FOPI n place of PI controller the change n Electromagnetc torque s further reduced from 0.86 to 0.04 pu and 0.25 to 0.01pu n case of STATCOM and UPFC

19 Page 19 of 20 Table 5 contnued 4. Change n Rotor Speed (per unt) Wthout SSR controller the rotor speed s changes from 1.05 to 1.28 tmes. The change n Rotor speed s reduced from to and to pu wth PI based STATCOM and UPFC controllers for a tme nterval of 1.05 to 10 s. The use of FOPI n place of PI controller the change n Rotor speed s further reduced from to pu and to wth STATCOM and UPFC By observng the Table 5 the FOPI based UPFC controller s more effectve and faster n mtgaton of Torque amplfcaton due to SSR as compared to PI based STATCOM, UPFC and FOPI based STATCOM controllers. Concluson In ths work, a robust Fractonal-order PI based STATCOM and UPFC controllers are developed to dmnsh the oscllatons n turbne-generator shaft due to torque amplfcaton effect of SSR. Based on the control system the mtgaton of synchronous resonance s acheved by rasng the dampng of network wth proper estmaton and njecton of synchronous component quanttes nto the lne usng UPFC and the results are compared wth STATCOM controller. For the system studed, the superorty of proposed FOPI based controller s demonstrated by comparng the results of conventonal PI controller for all cases. From the proposed study, t was observed that, fne and fast SSR mtgaton s acheved by Fractonal-order PI controller based UPFC as compared to conventonal PI based STATCOM, UPFC and Fractonal order PI based STAT- COM controllers. Moreover, the performance of proposed controller s evaluated under three-phase fault wth dfferent performance ndces namely; torque and mechancal stress between LPB-Generator, change n electromagnetc torque and change n rotor speed. Authors contrbutons DKR carred out the desgn of PI and FOPI based STATCOM and UPFC controllers to mtgate the SSR. BSU and ASJ performed the mathematcal analyss, mode shapes and domnant mode of turbne generator shaft under SSR condton. MPT, RM and CS performed the analyss of mechancal stress between LPB and Generator. All authors read and approved the fnal manuscrpt. Authors nformaton D. Koteswara Raju receved the B.Tech. degree n Electrcal and electroncs engneerng from JNTU Hyderabad, Inda and M.Tech. degree n Power system engneerng from Acharya Nagarjuna Unversty (ANU), Vjayawada, Andhrapradesh, Inda n 2006 and 2009 respectvely. He had been wth RVR&JC College of engneerng from June 2009 to May 2011 and Gudlavalleru engneerng college from June 2011 to Tll date as an Assstant professor n Electrcal and Electroncs Engneerng Department. At present he s pursng Ph.D. from Vsvesvaraya Natonal Insttute of Technology, Nagpur, Inda. Hs research nterests nclude power system protecton, operaton and control; Bhmrao S. Umre s workng as Assocate professor n the Department of Electrcal Engneerng, Vsvesvaraya Natonal Insttute of Technology Nagpur. He receved the B.E., M.Tech. and Ph.D. from Govt. College of Engneerng, Vsvesvarya Regonal College of Engneerng and RSTM of Nagpur Unversty, Inda n 1983, 1986 and 2009 respectvely. Hs research nterests nclude electrcal machnes, power system operaton, control and torsonal oscllatons; Anjal S. Junghare s workng as Assocate professor n the

20 Page 20 of 20 Department of Electrcal engneerng, Vsvesvaraya Natonal Insttute of Technology, Nagpur. She has receved the B.E., M.Tech. and Ph.D. from Vsvesvaraya Natonal Insttute of Technology, Nagpur, Inda n 1981, 1985 and 2008, respectvely. Her research nterests nclude control systems, power system operaton and control; Mohan P. Thakre receved the B.Tech. and M.Tech. degree n electrcal engneerng from Dr. Babasaheb Ambedkar Technologcal Unversty, Ragad, Inda, n 2009 and 2011, respectvely. He s awatng Ph.D. degree n power system protecton from Vsvesvaraya Natonal Insttute of Technology, Nagpur, Inda. Hs area of research nterest ncludes power system protecton, operaton and control ; Rambabu Motamarr receved the B.E and M.Tech n electrcal and electroncs engneerng and power electroncs and drves from Chatanya Engneerng College, Andhra Pradesh and Vsvesvaraya Natonal Insttute of Technology, Nagpur, Inda n 2010 and 2013 respectvely. Hs research nterests nclude applcaton of power electroncs n power system operaton and control; Chatanya Somu receved the M.Tech. n power electroncs and drves from Vsvesvaraya Natonal Insttute of Technology, Nagpur, Inda from Vsvesvaraya Natonal Insttute of Technology, Nagpur, Inda n At present he s workng as Assstant professor n EEE Department n Adtya Engneerng college, Kaknada, Andhrapradesh, Inda. Hs area of research nterest ncludes Applcaton of power electroncs n power system operaton and control. Author detals 1 Department of Electrcal Engneerng, VNIT, Nagpur, Maharashtra, Inda. 2 Electrcal and Electroncs Engneerng Department, Adtya Engneerng College, Kaknada, Andhrapradesh, Inda. Acknowledgements The authors are very thankful for the facltes provded by the Department of Electrcal Engneerng, VNIT, Nagpur to carry out ther research work. Competng nterests The authors declare that they have no competng nterests. Receved: 13 February 2016 Accepted: 30 June 2016 References Anderson PM, Agrawal BL, Ness JV (1989) Subsynchronous resonance n power systems. IEEE Press, New York Bongorno M, Svensson J, Ängqust L (2008a) Onlne estmaton of -synchronous voltage components n power systems. IEEE Trans Power Delvery 239(01): Bongorno M, Ängqust L, Svensson J (2008b) A novel control strategy for synchronous resonance mtgaton. IEEE Trans Power Electron 23(02): Bongorno M, Svensson J, Ängqust L (2008c) Sngle-phase VSC Based SSSC for synchronous resonance dampng. IEEE Trans Power Delv 23(03): Cao J-Y, Cao B-G (2006) Desgn of fractonal order controller based on partcle swarm optmzaton. Int J Control Autom Syst 4(06): Das Shantanu (2008) Functonal fractonal calculus for system dentfcaton and controls. Sprnger, Berln Hngoran NG, Gyugy L (2000) Understandng FACTS: concepts and technology of flexble ac transmsson systems. IEEE Press, New York IEEE, SSR Workng Group (1985) Terms, defntons and symbols for -synchronous oscllatons. IEEE Trans Power Appl Syst 06: Koteswara Raju D, Umre BS, Junghare AS, Thakre MP, Kale VS (2016) Mtgaton of Subsynchronous oscllatons wth common controller based statcom and SSSC. J Electr Eng Electron Technol 5(1):1 11 Kumar LS, Ghosh A (1999) Modelng and control desgn of a statc synchronous seres compensator. IEEE Trans Power Delvery 14(04): Kundur P (1994) Power system stablty and control. McGraw-Hll Inc., New York Padyar KR (1998) Analyss of -synchronous resonance n power systems. Sprnger, Berln Padyar KR, Prabhu N (2006) Desgn and performance evaluaton of -synchronous dampng controller wth STATCOM. IEEE Trans Power Delvery 21(03): Padyar KR, Swayam Prakash V (2003) Tunng and performance evaluaton of dampng controller for a STATCOM. Int J Electr Power Energy Syst 25: Panda S, Swan SC, Rautray PK, Malk RK, Panda G (2010) Desgn and analyss of SSSC-based supplementary dampng controller. Smul Model Pract Theory 18: Panda S, Balarsngh AK, Mahapatra S (2016) Supplementary dampng controller desgn for SSSC to mtgate -synchronous resonance. Mech Syst Sgnal Process 68 69: Pson E, Vsol A, Dormdo S (2009) An nteractve tool for fractonal order PID controllers. In: IECON proceedngs, pp Podlubny Igor (1999) Fractonal-order systems and PI λ D μ controllers. IEEE Trans Autom Control 44: Salemna A, Khederzadeh M, Ghorban A (2008) Mtgaton of synchronous oscllatons by 48-pulse VSC STATCOM usng remote sgnal. In: IEEE Bucharest Power Tech, pp 1 7 Thakre MP, Koteswara Raju D, Umre BS et al (2015) Study and mtgaton of synchronous oscllatons wth SSC based SSSC. J Power Energy Eng 03:33 43 Thrumalavasan R, Janak M, Prabhu N (2013) Dampng of SSR usng synchronous current suppressor wth SSSC. IEEE Trans Power Syst 28(01):64 74 Umre BS, Khedkar MK et al (2007) Applcaton of STATCOM for reducng stresses due to torsonal oscllatons n turbnegenerator shaft. In: IEEE conference, pp , Feb. 2007