Design and Simulation of Distributed Statcom Controller for Power Factor Improvement

Transcription

1 Design and Simulation of Distributed Statom Controller for Power Fator Improvement Swagat Satapathy M.Teh, Dept of EEE, Centurion University. Abstrat: The STATCOM is a stati reative power ompensator. It is onneted to the grid through a side reators and has a apaitor on the DC-link side. This DC-link apaitor is maintained at a given voltage under losed-loop ontrol while a set amount of reative urrent is fed aording to load requirements. The operating frequeny of the VSC is also ontrolled in a PLL (phase loked loop) manner. Hene, it is essential to have a losed-loop feedbak ontrol operation of the STATCOM. The state spae model of the STATCOM is non-linear. The non-linear model of the STATCOM is linearized. A linear model of the STACOM is proposed. In this model, the grid voltage and the fundamental omponent of the STATCOM VSC terminal voltage are assumed to be in-phase and the modulation index is kept within unity. PI-ontrollers for the ative and reative urrents as well as the DC-link voltage of the STATCOM have been designed. The model, with PI ontrollers has been simulated in MATLAB/SIMULINK environment with variation of the pre-harge voltage on the DC-link apaitor with linear loads (indutive). Improvement of the power fator of the grid urrent is ahieved for linear loads. Keywords: STATCOM (Stati Synhronous Compensator), Power Fator(PF), PI Controllers,swithed mode power supply (SMPS) Introdution: The Load are lassified as linear and non-linear loads. The linear loads are R, R-L, R-L-C,motors, heaters and inandesent lamps while non-linear loads are power eletroni apparatus like diodes or thyristor Prasanna Kumar Karjee Assistant Professor, Dept of EEE, Centurion University. retifiers, swithed mode power supply (SMPS), adjustable speed drives, ferromagneti devies, aring equipment s, indution heating systems et. As is well known, the urrent is proportional to the voltage in ase of a linear load whereas the urrent is not proportional to the voltage in ase of non-linear load. A linear load draws ative power from the grid with only fundamental omponent being present in the urrent and absorbs/injets reative power from/to the grid. However, a non-linear load draws ative power from the grid, where the urrent has fundamental and harmonis. These harmonis do not provide extra power but unneessarily, yet unavoidably, inrease the system volt-ampere (VA). This shows up as an inrease in the RMS urrent in the lines and leads to an extra heating of the transmission ondutors and system elements. The injetion of harmonis thus has a number of disadvantages, as reported in []. Hene, the ompensation of reative power is neessary for both linear and non-linear loads. Harmoni ompensation up to standard values [3],[4] and power fator improvement are main issues for suh loads The power fator PF is defined as the ratio of the ative powerp to the apparent power S. Thus PF= [P/S] (1) For purely sinusoidal voltage and urrent, the standard expression is obtained as PF=osφ() Whereosφ is popularly known as the displaement fator. The expression of the power fator is not validated for non-sinusoidal urrent due to non-linear load. Hene, for sinusoidal voltage and non-sinusoidal urrent, equation (1) an be expressed as: PF = V s,rms I s1,rms Cosφ V s,rms I s,rms (3) Page 137

2 = I s1,rms Cosφ I s,rms k p = I s1,rms I s,rms = Harmoni Content of the urrent and is 1 at best when there is no harmonis System Desription: Stati Synhronous Compensator (STATCOM): The STATCOM, in priniple, is a stati powereletroni version of the synhronous ondenser. It is a shunt-onneted reative power ompensation equipment as shown in Fig.1. It provides operating harateristis similar to a rotating synhronous ondenser. It has the advantage that it operates with a very fast transient response, thus appearing to be almost without any inertia, unlike the synhronous ondenser. It provides virtually step-less ompensation for reative VARs and maintains the desired power fator set as ontrol referene automatially, even in the event of load flutuations. It an be ontrolled to provide leading or lagging VARs and adjusts itself automatially as per load VAR requirement. In the event of inrease in plant load, putting additional units in parallel an inrease ompensation apaity. It is a low maintenane equipment. Fig : Relationship between vetors [17] Referring to Fig,The modeling of STATCOM is done by d-q transformation [5-15].Grid Voltage V s,ab lags STATCOM VoltageV o,ab phase angle differene of alpha (α). sin (wt ) v sa (t) V s,ab = [ v sb (t)] = V 3 s [ sin (wt π ) 3 ](4) v s (t) sin (wt + π ) 3 The Three Phase STATCOM urrent dynamis is represented in equation given below i a (t) i a (t) v sa (t) v oa (t) Ls d [ i dt b (t)] = Rs [ i b (t)] + [ v sb (t)] [ v ob (t)] i (t) i (t) v s (t) v o (t) (5) Negleting the urrent unbalane we have used a three-wire onnetion. The zero sequene omponent of urrent is zero as I a + I b + I = 0 (6) From Fig, resultant α-β omponents by transformation Fig 1: Shemati diagram of the STATCOM Generalised Modelling of Statom and Its Transformation [ x 1 α(t) 1 1 x β (t) ] = [ x a (t) ] [ x b (t)] (7) x (t) Where [x] abare phase quantities without zero sequene omponent and [x] αβ are equivalent transformed quantities. The α-β are orthogonal referene axes of dq rotating at an angular speed of ω rad/se, and is represented by following transformation Page 138

3 [ x d(t) (wt) ] = [sin x q (t) os (wt) os (wt) sin(wt) ] [x α(t) x β (t) ] (8) Where[x] dq are the set of equivalent transformed in ab o- dqreferene frame, the balaned three-phase ordinate axes are diretly transformed to orthogonal o-ordinate axes rotating at an angular speed are as follows: rad se x d (t) x a (t) [ x q (t)] = k [ x b (t)] (9) x 0 (t) x (t) WhereK k = 3 [ sin (wt) sin (wt π 3 ) sin (wt + π 3 ) os (wt) os (wt π ) os (wt + π ) (10) C.Swithing Of Converter: 1 ] We have assumed that harmoni omponents generated by swithing ation is negligible, and S as swithing funtion for three phase sin (wt) S a (t) S = = S b (t) m 3 [ sin (wt π ) 3 ] (11) sin (wt + π 3 [ S (t) ) ] Where m is modulation onversion index and is expressed as Modulation Index(m)= V 0,peak and is V d 3 multiplying fator in transformation of three phase stationary ab axes to rotating dq axes. The ative and Reative Power injeted/drawn to/by STATCOM is given by p (t) = v sd (t)i d (t) + v sq (t)i (t) = V s (t)i d (t) os + V s (t)i q (t) sin (1) q (t) = v sq (t)i d (t) + v sd (t)i q (t) is, = V s (t)i d (t) os V s (t)i q (t) sin (13) The states of, I d (s), I q (s) and (s) V d of the STATCOM are represented in frequeny domain as: = s 3 + s R s (14) I q (s) = (15) I d (s) V s [s os Ls + s ( R s L os w s Ls sin )] Ls + s R (w s R s L + m s ) + m d L s C d V s [s sin Ls + s ( R s L sin + w s Ls os ) + m V d (s) L s C d sin ] s 3 + s R s Ls + s R (w s L + m s ) + m R s d L s C d s os [ + ( R s d L os w s C d sin )] d = m V s s 3 + s R s Ls + s R (w s L + m s ) + m R s d L s C d (16) TABLE 1: PARAMETERS AND VARIABLES OF THE STATCOMSYSTEM SL N O MEANING 1 FUNDAMENTAL FREQUENCY FUNDAMENTAL ANGULAR FREQUENCY 3 RMS LINE LINE VOLTAGE SYMB OL F=F 1 Ω=Ω 1 V S VALUES 50hz 314rad/se 415v 4 EFFECTIVE R S 1.0Ω Page 139

4 COUPLING RESISTANCE [ V sd(t) V sq (t) ]=V s [ 1 0 ] (17) 5 COUPLING INDUCTANCE 6 DC-LINK CAPACITOR L S 5.44mh C DC 680µF d L s [i d(t) dt i q (t) ] = [ R s [ V od(t) V oq (t) ](18) ω 1 L s ω 1 L s ] [ i d(t) R s i q (t) ] + [V sd(t) V sq (t) ] 7 MODULATION INDEX(MODULAT ION CONVERSION INDEX 8 LOAD RESISTANCE M (M C) R L ( ) 3Ω For the above MIMO system we have onsidered input to be u and output to be y [u] = [ V od(t) V oq (t) ], [y] = [i d(t) i q (t) ](19) Design of Controller Current Controller 9 LOAD INDUCTANCE(WI TH ITS INHERENT RESISITANCE) L L (R L) 60MH(.06 Ω) The blok diagram of the losed-loop urrent ontroller is shown in and is repliated for both d and q axes urrents. Closed Loop Controller Design of STATCOM In this model as well as m (modulation index m is related to the modulation onversion index m as m = 3 m And hene a hange in m will hange m too both may are assumed to remain onstant at given values. Here, the grid side voltage and the STATCOM onverter terminal voltage are assumed to be in-phase 0 with eah other (as phase angle differene 0 ). Therefore this model is referred to as Model I. It is a modifiation over the model given in [16]. In that model, the authors have done on-line dynami omputation of and m. However, we have designed the ontrollers for the same model without omputing and m (as unity) 0 0 and m is within Fig 3: Generalized Blok Diagram of Current Controller The PI-ontroller bandwidth is hosen at 1kHz whih is 10 times slower than the swithing time of the STATCOM. The integrating time onstant, an be hosen to be smaller than the PWM swithing time of the STATCOM. Then the system operates faster but there is a possibility of saturation of the integrator. The Modified d-q Transformation of Grid Voltages and STATCOM urrents are represented below in their respetive equations as given by: DC Link Voltage Controller The blok diagram for the losed-loop ontrol of the DC-link voltage of the STATCOM is shown below Page 140

5 Fig 4: DC-link voltage ontrol loop The open loop transfer funtion G ov between the PI ontroller andv d The root lous of the transfer funtion is drawn by varying K pvm1 infinity. By hoosing the damping ratio K pvm1 is found as 1.84 from zero to 0.7 Controller Implementation In MATLAB Simulation: The blok diagram for pratial realization of the linear model proposed is given in Fig 7. In a 3-wire system, for obvious reasons, only two out of the 3- phase voltages on the grid side, two out of the 3-phase urrents of the STATCOM and two out of the 3-phase load urrents are sensed and feedbak. These 3-phase quantities are onverted to two-phase variables. The variables are then onverted to rotating d q variables with the help of unit vetors. For this, the instantaneous phase angle of these quantities needs to be dynamially estimated in a PLL fashion. The sensed v d referene voltage of is summed with (proper sign) the * V d and fed to a PI-ontroller. Thus, these ontrollers generate referenes whih are onverted bak to variables by help of unit vetors (inverse transformation). The gate pulses of the onverter are generated by SVPWM priniple using STATCOM onverter referene (stationary) o-ordinate voltages., Fig 5: Proposed ontroller tehnique of losed-loop system Controller Strategy: The entire ontrol (for both d -axis and q -axis ontrollers) is implemented as per the strategy of Fig 7. in real-time. Thus, these ontrollers generate referenes whih are onverted bak to variables by help of unit vetors (inverse transformation). The gate pulses of the onverter are generated by SVPWM priniple using STATCOM onverter referene (stationary) o-ordinate voltages. The above PI-ontrollers are implemented in MATLAB environment as given in Fig 8.The referene urrent is taken as the q omponent of the load urrent. Fig.6: Current Controlling Blok Simulation Results Page 141

6 Fig 9: System voltage and system urrent using Proportional ontroller Fig 7.Final Simulation done in MATLAB A linear load, simulated with parameters (given in Table 1)is onneted to the grid. The waveforms of the grid side phase-a voltage ( R L v sa ) and urrent ( i sa ) at point of ommon onnetion (PCC) (without the STATCOM in operation) are shown in Fig.4.4. It may be mentioned that here and elsewhere (unless otherwise mentioned) v sa is plotted to a redued sale 10 :1. Under steady state it is seen that the power of angle is 39.64(so that power fator is 0.77). The STATCOM will now at in losed-loop with this system along with the proposed ontrollers in order to improve this power fator. Fig 10: System voltage and STATCOM urrent using Proportional ontroller Fig 11: Ative and Reative power generated by STATCOM Fig.8 Grid phase-a voltage and urrent with R L load before operation of the STATCOM Fig1: DC link voltage using Proportional ontroller Page 14

7 Fig 16: System voltage and system urrent using Proportional ontroller Fig 13: DC link urrent using Proportional ontroller Fig 17: System and STATCOM output voltage using Proportional ontroller Fig 14: System and STATCOM output voltage using Proportional ontroller Fig 18: System voltage and system urrent using PI ontroller Fig 15: DC link voltage due to hange of referene urrent using Proportional ontroller Fig 19:System voltage and STATCOM urrent using PI ontroller Page 143

8 Fig 0: DC link voltage using PI ontroller Fig 3: System and STATCOM output voltage using PI ontroller Fig 1: DC link urrent using PI ontroller Fig. 4: System voltage and system urrent using PI ontroller with 700DC link voltage Fig : DC link voltage due to hange of referene urrent using PI ontroller Fig 5: DC link urrent using PI ontroller with 700DC link voltage Page 144

9 Conlusion: A linear model of the STATCOM is proposed onsidering the grid voltage to be in-phase with the fundamental omponent of the STATCOM onverter output voltage. The PI-ontrollers have been designed with relation to the parameters of the STATCOM and based on root lous method after linearizing the nonlinear model of the STATCOM. The strategy has been simulated using MATLAB/SIMULINK environment for different pre-harge voltage on the DC-link, with linear load. The STATCOM is applied for improving the power fator of the grid urrent in this ase. Referenes: [1] Vikram Kaura, Operation of a Phase Loked Loop System Under Distorted Utility Conditions [] T.Hoevenaar, K.LeDoux and M.Colosino, An introdution to Power system harmonis, Copyright Material IEEE, Paper No.PCIC , pp.1-6, 003. [3] Power System Harmonis Causes and Effets of Variable frequeny Drives Related to the IEEE Standard, Bulletin No.8803PD940, pp.1-8, Raleigh, NC, USA, Aug.1994 [4] J.K.Piel and D.J.Carnovale, Eonomi and Eletrial Benefit of Harmoni Redution Methods in Commerial Failities, PU E, pp.1-9, July 004. [5] C.T.Rim, D.Y.Hu and G.H.Cho, Transformer as equivalent iruit for swithes: General proofs and D-Q Transformation-based Analyses, IEEE Transations on Industry Appliations, Vol.6, No.4, pp , July [6] G.C. Cho, N.S. Choi, C.T. Rim and G.H. Cho, Modeling, Analysis and Control of Stati Var Compensator using Three-Level Inverter, IEEE, Industry Soiety Meet,pp ,199. [7] G.C. Cho, G.H. Jung, N.S. Choi and G.H. Cho, Analysis and Controller Design of Stati Var Compensator Using Three-Level GTO Inverter, IEEE, Transations on Power Eletronis, Vol.11, No.1, pp.57-65, Jan [8] A. Tahri, A. Draou and M. Benghanem, A Fast Current Control Strategy of a PWM Inverter used for Stati VAR Compensation, IEEE IECON onferene, pp , [9] M.H.Rashid Power Eletronis Hand Book Aademi press Harourt Siene and Tehnology Company, Tokyo, Multilevel Converter and VAR ompensation by A.Draou and A.Tahri, pp ,001. [10] Tahri, A. Draou and M. Benghanem, Performane Analysis of Advaned STATIC VAR ompensator using three-level IGBT Inverter, IEEE IECON Conferene, pp , [11] J.K.Moharana, M.Sengupta, A.Sengupta Study on an Advaned Stati Var Compensator swithed from a Spae Vetor PWM inverter-analysis, Simulation and Comparison with the onventional Sinusoidal PWM ase, NPEC003, IITB, pp.7-78, 003. [1] J.K.Moharana, M.Sengupta, A.Sengupta A Nonlinear Control Modeling of A STATCOM for Reative Power Compensation, NPSC-004, IITM, pp , 004 [13] J.K.Moharana, M.Sengupta, A.Sengupta Design and Simulation of Current Controller and Voltage Controller for A STATCOM Appliation, NPEC005, IITKGP, pp , 005. [14] J.K.Moharana, M.Sengupta, A.Sengupta Modeling, Analysis and Simulation of Various Control Strategies for a 6kVA STATCOM for reative power ompensa`tion, NPEC-007, IIS, Bangalore, 007 [15] J.K.Moharana, M.Sengupta, A.Sengupta Closed- Loop Control of a lab-sale STATCOM prototype for Reative Power Compensation, ommuniated to NPEC-011, BESU, Shibpur, Howrah, West Bengal, 011. [16] C. Shauder and H.Mehta, Vetor analysis and Control of Advaned Stati VAR Compensator, IEE Proeedings-C, Generation, Transmission and Distribution, Vol.140, No.4, pp , July, Page 145