Tuned PI Controller usng Zegler-Nchols Method for Power Qualty Enhancement for lnear and non lnear s Rtu Sharma Department of Electrcal Engneerng, Gurgaon Insttute of Technology & Management, Gurgaon Emal: rtu98@gmal.com Abstract-In ths paper, a -leg oltage source nerter (VSI) based Dstrbuton Statc Compensator (DSTATCOM) s used for compensaton n -phase - wre dstrbuton system. The control algorthm s based on Synchronous Reference Frame (SRF) algorthm. Ths algorthm s used for extractng the reference source currents for oltage regulaton at pont of common couplng (PCC), balancng and harmonc reducton. For arous condtons such as a reacte lnear, an unbalanced and a non-lnear, smulatons are performed for oltage regulaton(vr) mode n MATLAB enronment usng SIMULINK and SmPower system toolbox. Tunng of PI (Proportonal Integral) controller s done usng tral and method and Zegler Nchols(Z-N) method. Index Terms control algorthm, DSTATCOM, nonlnear,power qualty, Zegler-Nchols method. I. INTRODUCTION Electrc power qualty [1] s a term whch has captured ncreasng attenton n power engneerng n the recent years. Electrc power qualty means dfferent thngs for dfferent people. Good power qualty for an electrc motor may not necessarly be good enough for a personal computer. The waeform of electrc power at generaton stage s purely snusodal and free from any dstorton. Many of the power conerson and consumpton equpment are also desgned to functon under pure snusodal oltage waeforms. Howeer, there are many deces that dstort the waeform. These dstortons may propagate all oer the electrcal network. In recent years, there has been an ncreased use of non-lnear s whch has resulted n an ncreased fracton of nonsnusodal currents and oltages n electrc network. In present tme, dstrbuton system s facng the poor power qualty problems such as poor power factor, unbalanced ng of three phases, oltage drop and harmonc njecton. The reasons for the poor power qualty are reacte, unbalanced and nonlnear s used n domestc and ndustral applcatons. Such power qualty problems can be mtgated by connectng the DSTATCOM at the pont of common couplng (PCC). In ths paper, SRF algorthm s used for oltage regulaton at PCC, balancng and harmonc reducton []. In a DSTATCOM, the dc capactor oltage and ac oltage are regulated usng PI controllers. The performance of the compensator s healy affected by the proportonal and ntegral gan settngs of the PI controller. Conentonally, a PI controller s tuned usng tral and method whch s tme consumng and also may not yeld good results. A Zegler Nchols method s explored here and performance of the same system s tested under arous condtons. II. SYSTEM CONFIGURATION The basc crcut dagram of a three phase three wre DSTATCOM s shown n Fg.1.The model s deeloped for a three-phase, three-wre system confguraton. DSTATCOM conssts of three-phase Insulated Gate Bpolar transstor (IGBT) based oltage source nerter (VSI) wth small flter capactors and DC bus capactor. The three-phase IGBT based VSI has three nput nductors and an electrolytc capactor at ts DC lnk. Threephase ac mans wth lne mpedance feed power to three phase s. Three phase s may be a lnear balanced / unbalanced or a non lnear balanced/unbalanced. The DSTATCOM s controlled wth SRF algorthm for regulatng the oltage at PCC, balancng and harmonc reducton. DSTATCOM regulates the PCC oltage at the desred reference alue of the oltage by njectng the requred reacte power. Fg.1. Block dagram representaton of DSTATCOM for three phase three wre system III. CONTROL SCHEME The PI controllers as well as SRF controller are deeloped for oltage regulaton at PCC. These two current control schemes are used to estmate ampltude of reference supply current. Once the reference currents are generated, hysteress current controller s desgned to obtan approprate gatng sgnals. These gatng pulses prode swtchng on and off of sx IGBT swtches of the oltage source nerter workng as a DSTATCOM. A. Synchronous Reference Frame Theory Synchronous reference frame (SRF) theory based controller noles sensng of currents and lne oltag- 69
es []-[6]. The nstantaneous currents are splt nto acte and reacte components by usng Clark s and Park s transformatons. The Clark s transformaton s used to conert -phase currents to -phase currents n statonary frame whch are also called α-β components ( α, β ) and Park s transformaton s used to conert these currents n statonary frame ( α, β ) to synchronously rotatng frame whch are also known as d-q components ( d, q ).The d-component ( d ) s acte power component and q-component ( q ) s reacte power component of currents. The acte and reacte power components of fundamental reference source currents are generated by subtractng the reacte power component of currents from output of the oltage controller. These acte and reacte power components of reference source currents are used to generate three-phase fundamental reference source currents( sa, sb, sc ) by usng nerse Park s and Clark s transformatons. A schematc dagram of SRF theory based control algorthm s shown n Fg.. Reference source currents ( sa, sb, sc ) are compared wth sensed source currents ( sa, sb, sc ) n order to generate sgnals for gatng of IGBTs of VSC. B.Computaton of Phase Voltages and Reference Source Currents Phase oltages are computed from any two lne oltages ( ab, bc ) sensed at PCC. a b c 1 1 1 1 ab (1) 1 bc The ampltude of termnal oltage s calculated from nstantaneous phase oltages as n Eq (). t a b () c The acte and reacte components of currents are extracted by sensng currents ( La, Lb and Lc ) as well as oltages at pont of common couplng (PCC). Frst sensed three phase currents are conerted to two phase currents( α, β ) n statonary frame usng Clark s transformaton as shown n Eq(). 1 1 1 These currents are conerted to synchronous rotatng d-q reference frame ( d, q ) components usng Park s transformaton as under 1 1 1 La Lb Lc La Lb Lc () (4) where θ s transformaton angle and snθ and cosθ are obtaned from phase oltages usng PLL. The d-q components are then passed through low pass flters n order to extract only DC components of current ( ddc, qdc ). Then reacte component s subtracted from output of oltage PI controller to generate reacte power component ( qdc ) of reference source currents. The output of PI oltage controller s estmated reacte power component of DSTATCOM current. The nput to the PI controller s the oltage whch s defned as t ( n) ( n) ( n) (5) tref where, V tref (n) the reference termnal phase oltage and V t (n) s the nstantaneous phase oltage at pont of common Couplng(PCC).V t (n) s obtaned usng ().At the n th samplng nstant, the output of the oltage controller s gen as qdst k ( n 1) ( n) ( n 1) ( n) (6) p k where, K p and K are gan parameters of the oltage PI controller.so, the nstantaneous alue of the ampltude of the fundamental reacte power component of reference source current s as qdc qdst (7) qdc The acte component s kept wthn 8% to 1% of rated current to generate acte component of reference source currents. The acte and reacte components of reference source currents are then used to generate threephase reference source currents by usng nerse Park s and Clark s transformatons as shown n Eq(8) and Eq(9). Usng nerse Park s transformaton cos sn dc ddc (8) sn cos dc qdc Usng nerse Clark s transformaton sa sb sc 1 1 1 dc dc Fg.. SRF based control algorthm (9) These reference source currents ( sa, sb, sc ) are compared wth sensed source currents( sa, sb, sc ) n hysteress current controller n order to generate sgnals for gatng of IGBTs of VSC. 7
C. Desgn of Hysteress Controller Hysteress controller for trackng of reference source currents s shown n fg.. [7]The sgnals of the reference and the actual source currents are determned and compared wthn hysteress band generally 1% to 5% of the current leel. The control logc used s gen as If ( sa < sa - h b ), then the upper swtch of VSC s turned OFF and lower swtch s turned ON The upper and the lower swtchng dece (IGBT n our model) are swtched ON and OFF n a complementary fashon. The hysteress band h b can be ared. A narrow hysteress band results n ery good and fast trackng of currents but swtchng frequency may become too hgh. A wde hysteress band may not prode effecte trackng thus leadng to the system becomng unstable. IV. TUNING OF PI CONTROLLERS Tunng of PI controller s done usng tral and method and Z-N method [8],[9].Tunng the parameters for the PI controller can be a challenge, and f the tme constants n the process are huge, the tme to do the optmzaton could be too long. But there s some rule of thumb, of whch the rule lned out by Zegler-Nchols back n 194[9] s well known. A. Zegler-Nchols method Procedure for Zegler Ncolas method s as follows: 1) Turn off the I-term and the D-term n the controller. ) Turn K P =, and the ncrease t slowly, whle lookng at the controllable arable (y) or - some tmes better - the output of the controller, u. Increase K P untl the output exhbts sustaned oscllatons. ) At ths "quas steady-state" pont K P,crt =K_P_crt, called the crtcal gan, and a gen perod of tme, T crt =T_crt. 4) Then turn on the I- and D-term by usng the followng alues, K p =.45K P,crt ; K = T crt /1.17. IV. MATLAB BASED MODEL AND PERFORMANCE MATLAB based models of three phase three wre grd connected system feedng lnear, non lnear and balanced, unbalanced hae been deeloped and performance of these hae been studed for dfferent condtons. The lnear s modeled and smulated n the form of RL and the non-lnear s modeled and smulated n the form of three phase dode brdge rectfer feedng resste. Both the power crcut as well as approprate controller (PI and SRF) are deeloped usng Smulnk and Powersystem toolbox of MATLAB. Fg.4 shows the MATLAB model deeloped for three phase three wre system wth lnear and non lnear s. Results of the deeloped MATLAB model wth lnear and non lnear s and dfferent methods of PI tunng are presented n Fgs.5 (a)-5(d). Fg.. Schematc representaton of Hysteress Controller Fg.4. MATLAB based model for the system A. Performance of DSTATCOM n oltage regulaton mode 1. Wth Lnear Reacte The performance of DSTATCOM n VR mode wth SRF s shown n Fg. 6(c). At t=.sec, three phase lnear s changed to two phase and reappled at t=.4sec. At.sec s ncreased from 9KW to 1KW and agan changed to 9 KW at.5sec.the PCC oltages (Vabc), source currents (Isabc), currents (ILoad), DSTATCOM currents (Istatcom), and DC bus oltage (Vdc ) are shown n Fg. 5(a) and Fg.5(b).It s obsered that the PCC oltage s regulated to ts reference ampltude of the PCC oltage and the source currents are balanced een when the s are unbalanced. As the requred reacte power to regulate the PCC oltage s njected by the DSTATCOM and s compensated by the DSTATCOM.. Wth Nonlnear Load The performance of DSTATCOM n VR mode for a nonlnear s shown n Fgs.5(c) and 5(d). The nonlnear s are compensated by the DSTATCOM to shape the source currents harmonc free and balanced durng balanced/ unbalanced and ncreased nonlnear s. The controller regulates the PCC oltage and DC bus oltage of DSTATCOM to ther reference oltage. The waeform and harmonc spectra of source oltage, source current and current s shown n Fgs.6 (a) and Fgs.6 (b). The source oltage THD s.% and the THD of source current s found14.9% when the THD of current s 6.55% for PI tunng wth tral and method as shown n Fgs.6 (a). The source 71
oltage THD s.1% and the THD of source current s found.95% when the THD of current s 8.75% for PI tunng wth Zegler-Ncolas method as shown n Fgs.6 (b). 5 5-5.15..5..5.4.45 Tme(sec) -.15..5..5.4.45 Tme(sec) -5.15..5..5.4.45 Tme(sec) 5-5.15..5..5.4.45 Tme(sec) 8-8.15..5..5.4.45 Tme(sec) 1 8 6 4.1...4.5.6 Tme(sec) 4.1...4.5.6 Tme(sec) Fg.5 (a).performance of DSTATCOM n Voltage regulaton mode controlled by SRF algorthm and PI tunng wth tral and method wth lnear balanced/ unbalanced/ncreased 5-5.15..5..5.4.45 Tme(sec) -.15..5..5.4.45 Tme(sec) 1 5 4.1...4.5.6 Tme(sec).1...4.5.6 Tme(sec) Fg.5(d). Performance of DSTATCOM n Voltage regulaton mode controlled by SRF algorthm and PI tunng wth Zegler-Nchols method wth nonlnear balanced/unbalanced/ncreased - 1.5 1 FFT wndow: of 9.67 cycles of selected sgnal.1.15.11.115.1.15.1.15 Tme (sec) x 1 - Fundamental (5Hz) = 8., THD=.1% 5-5.15..5..5.4.45 Tme(sec) 1.5 4 6 8 1 1 14 16 18 Harmonc order -1.15..5..5.4.45 Tme(sec) 5 FFT wndow: of 9.67 cycles of selected sgnal 8 6 4.1...4.5.6 Tme(sec) 4-5.1.15.11.115.1.15.1.15 Tme (s) Fundamental (5Hz) = 59, THD=.95%.1...4.5.6.7.8.9 1 Tme(sec) Fg5. (b). Performance of DSTATCOM n Voltage regulaton mode controlled by SRF algorthm and PI tunng wth Zegler Nchols method wth lnear balanced/unbalanced/ncreased 5-5.15..5..5.4.45 Tme(sec).8.6.4. 5 5 1 15 Harmonc order FFT wndow: of 45.18 cycles of selected sgnal -.15..5..5.4.45 Tme(sec) -.15..5..5.4.45 Tme(sec) -5.1.15.11.115.1.15.1.15 Tme (s) Fundamental (5Hz) = 57.7, THD= 6.55% 15 1 8 6 4.1...4.5.6 Tme(sec) 5 5 1 15 Harmonc order 4.1...4.5.6 Tme(sec) Fg.5(c). Performance of DSTATCOM n Voltage regulaton mode controlled by SRF algorthm and PI tunng wth tral and method wth nonlnear balanced/unbalanced/ncreased Fgs.6(a).Waeform and THD spectrum of source oltage of phase a,source current of phase a, current of phase a n Voltage Regulaton mode wth PI tunng usng tral and method. 7
FFT wndow: of. cycles of selected sgnal -.1.15.11.115.1.15.1.15 Tme (s) PI gans Kpd=.,Kd=8, Kpa=.11,Ka=.8 Kpd=.,Kd=4.1,K pa=.11, Ka=.8 1.5 1.5 5-5.8.6.4. 5-5 15 1 5 x 1 - Fundamental (5Hz) = 8., THD=.1% 5 1 15 Harmonc order FFT wndow: of. cycles of selected sgnal.1.15.11.115.1.15.1.15 Tme (s) Fundamental (5Hz) = 59, THD=.95% 5 1 15 Harmonc order FFT wndow: of. cycles of selected sgnal.1.15.11.115.1.15.1.15 Tme (s) Fundamental (5Hz) = 58.19, THD= 8.75% 5 1 15 Harmonc order Fgs.6 (b).waeform and THD spectrum of source oltage of phase a,source current of phase a, current of phase a n Voltage Regulaton mode wth PI tunng usng Zegler Nchols method. TABLE I : Comparson of PI tunng methods Parameters PCC Voltage DC lnk oltage Methods Tral and method Regulates to reference alue Regulates to reference alue 8V acheed Load balancng Harmonc reducton THD of source oltage THD of source current THD of current Zegler-Nchols method Regulates to reference alue Regulates faster to reference alue 8V acheed Source currents Source currents are are balanced and balanced and snusodal.thd snusodal.thd s s 14.9%.95%.%.1% 14.9%.95% 6.55% 8.75% V. CONCLUSION The smulaton and mplementaton of DSTATCOM wth the SRF algorthm and PI tunng usng tral and method and also by Zegler-Nchols method hae been carred out for the compensaton of lnear balanced/unbalanced and nonlnear balanced/ unbalanced n three phase three wre dstrbuton system. The oltage regulaton mode of DSTATCOM has been acheed for compensaton wth SRF algorthm and two dfferent methods of PI controller tunng. The DC bus oltage of DSTATCOM has been regulated to ts reference alue for arous ng condtons. In smulaton, t s found that the performance and response of controller s fast and effecte n oltage regulaton mode for compensatng the lnear balanced/unbalanced and nonlnear balanced/unbalanced usng Zegler-Nchols method for PI controller tunng. VI. APPENDIX AC lne oltage 415V (L-L), 5Hz; source resstance: Rs=.1Ω; lne mpedance: R=.5 Ω, L=1 mh; oltage source conerter: DC lnk oltage 8V,DC capactor 15μF, nterfacng nductor.mh, for rpple flter :R r = Ω,C r =1μF; lnear : phase S 1 =9kW,S =1KW; non lnear : phase brdge rectfer wth R 1 =1.5Ω, R=7 Ω. REFERENCES [1] Veeraah Kumbha and N. Sumath, Power qualty mproement of Dstrbuton lnes usng DSTATCOM under arous ng condtons,internatonal Journal of Modern Engneerng Research, ol., ssue. 5, pp.451-457, Sep.-Oct. 1. [] K. R. Padyar, FACTS Controllers n Power Transmsson and Dstrbuton, New Age Internatonal (P) Lmted, Publshers, New Delh, 7. [] Bhm Sngh, and Jtendra Solank, A Comparson of Control Algorthms for DSTATCOM, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, ol. 56, no.. 7, 9,pp.78-745. [4] Bhm Sngh, Alka Adya, A.P.Mttal and J.R.P. Gupta, Modelng, Desgn and Analyss of Dfferent Controllers for DSTATCOM, Jont Internatonal Conference on Power System Technology and IEEE Power Inda Conference, 8,pp.1-8. 7
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