Dynamics and Control of Three-Phase Four-Leg Inverter

Transcription

1 RECENT ADVANCES in ELECTRONICS HARDWARE WIRELESS an OPTICAL COMMUNICATIONS Dynamics an Control of Three-Phase Four-Leg Inverter JENICA ILEANA CORCAU Avionics Division University of Craiova Faculty of Electrical Engineering 7 Decebal Blv. 44 Craiova Dolj jcorcau@elth.ucv.ro jcorcau@yahoo.com TEODOR LUCIAN GRIGORIE Avionics Division University of Craiova Faculty of Electrical Engineering 7 Decebal Blv. 44 Craiova Dolj lgrigore@elth.ucv.ro NICOLAE JULA Military Technical Acaemy 8-83 G. Cosbuc Blv. Sector 5 Bucharest nicolae.jula@gmail.com COSTIN CEPISCA Electrical Engineering Faculty University POLITEHNICA of Bucharest 33 Splaiul Inepenentei Sector 6 Bucharest costin@wing. ro NICOLAE POPOVICIU Hyperion University 69 Calea Calarasilor Sector 3 Bucharest nicolae.popoviciu@yahoo.com Abstract: In this paper the moelling an analysis of three-phase four-leg inverter are presente. Also this paper presents two strategies of control an their limitations. The frequency characteristics of the system are useful for etermining its control strategies. Initially a PI compensator is use. Finally the control esign strategy using 4zeros/5poles is chosen as optimum strategy. The system operation is verifie for loa variation from % to % rate loa. The close loop performances of the inverter are verifie using the Matlab/Simulink software package. Key-Wors: - Three-phase four-leg Uninterruptible Power Supply Power istribution system control strategy. Introuction The main feature of a three phase inverter with an aitional neutral leg is the ability to eal with unbalance loa in a stanalone power supply system []. The goal of the three-phase four-leg inverter is to maintain the esire sinusoial output voltage waveform over all loaing conitions an transients. This is ieal for applications like ata communication ISSN: ISBN:

2 RECENT ADVANCES in ELECTRONICS HARDWARE WIRELESS an OPTICAL COMMUNICATIONS inustrial automation military equipment which require high performance uninterruptible power supply (UPS). Figure presents the scheme of the switche inverter moel with four conuctors []. The fourth conuctor (N) permits the control of the neutral current. For the three-phase inverters if the loa requires us to connect the null we utilize the null point of the capacitor filter of the c connection [] [3]. In this case the unbalance loas or the non-linear single phase loas generate null currents an istortions when passing through zero. When using inverters with four terminals (A B C an N) the control over the null is obtaine an the zero istortions cause by the inverter control system are reuce. + - V in L filter C filter Fig. The scheme of the switche inverter moel with four conuctors In figure ([]) is presente the three-phase four-leg inverter use in the shipboar c PDS (Power Distribution System) to provie seconary AC power istribution. It can be use to supply utility power for combat equipments raar an other critical electronic loas []. L n A B C N Power stage moelling of the threephase four-leg inverter Generally in the literature three levels of moels are available for inverter system: etaile moel behavioral moel an reuce orer moel. The etaile moel is base on equations erive from the system structure an electrical circuit [4]. An example of a etaile moel for a three-phase fourleg inverter woul be a moel that exactly escribes all voltage an current waveforms in circuit prouce by the switching action of the semiconuctor switches. A etaile moel requires a very long time for numerical simulation. So a etaile moel often inclues iscrete an iscontinuous functions an it cannot be use for control loop esign base on linearization an frequency omain analysis techniques. For this reason a etaile moel is use only in simulations when a etaile stuy of the system operation is require. The behavioral moel is erive from the etaile moel by time averaging of high frequency perioical waveforms such as switching waveforms [4]. The behavioral moel of inverter is calle average moel. The reuce orer moel is obtaine from the behavioral moel by its linearization at an equilibrium point. So it is often calle linearize moel. A large signal moel is reuce to a small signal moel which is available in the vicinity of this operating point only. The Matlab/Simulink software package can performs automatically this linearization using the linmo comman. The average moel of the three-phase fourleg inverter in steay-states coorinates is shown in figure 3 ([5]). Fig. The iagram of Power Distribution System (PDS) The PDS comprises of a front-en boost rectifier feeing the c link an various loas connecte to the c link which inclues a three-phase four-leg inverter an a c to c power converter. Fig. 3 The average moel of inverter The moel is obtaine replacing the switches with controlle voltage an current sources. ISSN: ISBN:

3 RECENT ADVANCES in ELECTRONICS HARDWARE WIRELESS an OPTICAL COMMUNICATIONS The inverter output voltage an input current can be represente as [5] an a n V bn b n = () V c n cn I a I [ ] p = an bn cn I b () I c where V in (i=a b c ) are the inverter outputs voltages (line-neutral) I a I b I c are line currents an in (i=a b c) are the line-to-neutral uty cycles. The uty cycles in (i=a b c) are controlle to prouce sinusoial voltages at the filter output as a function of the loa; the loa coul be light heavy unbalance or non-linear. The system requirements can be represente as an cos( ωt) o cos( ) Vbn = Vm ωt (3) o V cos( ωt+ ) cn where V in (i=a b c) is the output loa voltage an V m the rate output voltage. To prouce the esire sinusoial output voltages the steay-state uty cycles are time-varying an sinusoial. But to apply classical control techniques a DC operating point is necessary. As a consequence to get the power stage moel in rotating coorinates the transformation T is applie. In this way the steay-state output loa voltages an the uty cycles are c quantities being escribe as follows m = Vq (4) V an ( ω ) / D LC Vm ω LI = Dq. V (5) g D The parameters on three-phase four-leg inverter are []: V L-N = 77 Vrms L = 333 µh C = µf V DC = 8 V P = 5 kw f s = khz f = 6 Hz. The loa of the inverter is represente as a isturbance an is consiere resistive. The output varies from % to % rate power so loa varies from.53 Ω to 53 Ω. The average large signal moel is simulate using the Matlab/Simulink software package. In orer to obtain the small signal moel the average moel is processe with linmo Matlab comman aroun an operating point in the small perturbations hypothesis; the small signal moel is necessary in the control esign phase. The Boe iagrams for system open loop control in the light loa case are presente in figure 4. Figure 5 epicts the same characteristics for heavy loa case. Fig. 4 The Boe iagrams for system open loop control in the light loa case Fig. 5 The Boe iagrams for system open loop control in heavy loa case Neglecting the coupling in the power stage the open loop transfer function is approximate as V V g H (s) = (6) + ( L / R) s+ ( L C) s This transfer function can be replace with a seconegree low-pass filter by the form H ( s) = (7) + s /( Q ω ) + (s / ) ω ω = (8) L C Q= R C / L (9) ISSN: ISBN:

4 RECENT ADVANCES in ELECTRONICS HARDWARE WIRELESS an OPTICAL COMMUNICATIONS ω =. () L C ω is the resonant frequency (approximately 87 Hz) an Q is the circuit quality factor. Accoring with the equation (9) Q is a function of the resistive loa so Q is larger when R is larger. It can be observe that the amplitue-frequency characteristic epicte in figure 5 presents a peak between 3 ra/sec an 4 ra/sec. The controller is esigne to satisfy the system performance for both heavy an light loa cases. 3 Control loop esign In figure 6 is presente the close loop moel of the inverter implemente in Matlab/Simulink. The output filter capacitor voltages are sense an transforme from stationary to rotating coorinates. These are use as feeback signals for -q- channels voltage compensators. The voltage loop gain T v is V Tv ( s) = H v (s). () The three-phase four-leg inverter is a multi loop an highly couple multi-variable system [7]. The -q- channels compensators are esigne inepenently with the other channels assume as open (q an channels). In the first stage a PI compensator was use (esign I) ([6]) K s (s) = + i K = i H v K p + () s s K i / K p where the coefficients are chosen with the numerical values K p =.5-5 an K i =.7. The Boe iagrams for the system using the PI controller in the heavy loa case are presente in figure 7. Also it can be observe that the amplitue-frequency characteristic presents a peak between 3 ra/sec an 4 ra/sec. Closing the loop gain below the resonance yiels low system banwith an this results in a poor transient response. Another possibility is to close the system loop after resonance [8] [9]. The finally chosen compensator architecture is 4zeros/5poles (esign II) with zeros place at z = 78 Hz z = 8 Hz z 3 = 8 Hz z 4 = 84 Hz an poles p = khz p =.5 khz p 3 = khz p 4 = Hz p 5 = Hz. The Boe iagrams for this control architecture are presente in figure 8. The Boe iagrams for the same control architecture but with heavy loa are shown in figure 9. Fig. 7 The Boe iagrams for the system using the PI controller in the heavy loa case q Gain Transfer Fcn numc (s) enc (s) C.s Gain 3 C.s Gain 7 Gain Gain 4 Gain 8 L.s L.s il ilq Gain 9 Gain 6 Gain Gain 5 Out To Workspace Step Out V To Workspace Freq Sin_Cos wt Discrete Virtual PLL q sin_cos abc q _to_abc Transformation Vabc To Workspace3 Vq Constant 3 num (s) en (s) Gain (L+3*Ln )s C.s Gain 3 Out 3 V To Workspace Fig. 6 The close loop moel of the inverter ISSN: ISBN:

5 RECENT ADVANCES in ELECTRONICS HARDWARE WIRELESS an OPTICAL COMMUNICATIONS Figure shows the plots in time of V an V q with light loa an figure - with heavy loa. The compensator is esigne in rotating coorinates an hence it controls V an V q. The final output voltage is erive from them after applying the transformation T. In figure are presente the plots in time of V a V b an V c. The V turns out to be in these simulations as the loa is taken as the balance loa. Fig. 8 The Boe iagrams for compensator with 4zeros/5poles Fig. V an V q for heavy loa case Fig. 9 The Boe iagrams for compensator with 4zeros/5poles an heavy loa Fig. The plot in time of V a V b an V c. Control esign II is superior to esign I as the cross over frequency in case II is much higher than in case I. Dynamic simulations of inverter employing strategy I shows that the settling time for an output loa voltage is higher. Fig. V an V q for light loa case 4 Conclusions In this paper the moeling an control of three-phase four-leg inverter is presente. Two control strategies are presente in this paper. The performances of inverter are verifie through simulation using the Matlab/Simulink software package. As is shown in figure 5 for system open loop control in heavy loa case there is a large peak. Also the presence ISSN: ISBN:

6 RECENT ADVANCES in ELECTRONICS HARDWARE WIRELESS an OPTICAL COMMUNICATIONS of a similar peak can be observe on the amplituefrequency characteristic for the system using the PI controller in the heavy loa case (figure 7). So control esign II (4zeros/5poles compensator) is superior to esign I (PI compensator) as the cross over frequency in case II is higher than case I (see figures 8 an 9). Dynamic simulations of inverter employing strategy I shows that the settling time for an output loa voltage is higher. References: [] I. Aron J. Corcau Moeling an analysis of a c power istribution system. The 3th Session of scientific presentation Moern technologies in the XXI Century Bucuresti 6-7 November 3 pp. 9-5 CD. [] G.S. Thani Moeling Control an Stability of a PEBB base c istribution power System. Master of Science in Electrical Engineering 997. [3] U. N. Jensen A new control metho for 4Hz Groun Power Units for Aircraft. IEEE Transactions on Inustry Applications vol. 36 no. pp [4] K. Louganski Moeling an analysis of a c power istribution system in st century air lifters. Master of Science in Electrical Engineering 999. [5] R. Zhang High performance power converter system for non-linear an unbalance loa source. Dissertation Virginia Tech 998. [6] M.N. Rashi Power Electronics Circuits Devices an Application. Secon Eition 99. [7] Y. Han A.G. Yao L.D. Zhou C. Chen Design an Experimental Investigation of a Three-Phase APF base on Fee-Forwar plus Feeback Control. WSEAS TRANSACTIONS on POWER SYSTEMS Issue Volume 3 February 8. [8] N.Y.A. Shammas S. Eio D. Chamun Semiconuctor Devices an Their Use in Power Electronic Applications WSEAS TRANSACTIONS on POWER SYSTEMS Issue 4 Volume 3 April 8. [9] Y. HAN M.G. Yao L.D. Zhou C. Chen Harmonic Mitigation of Resiential Distribution System using a Novel Hybri Active Power Filter WSEAS TRANSACTIONS on POWER SYSTEMS Issue Volume December 7. ISSN: ISBN: