A Single-stage Three-phase DC/AC Inverter Based on Cuk Converter for PV Application

Transcription

1 A Singlestage Threephase D/A Inverter Base on uk onverter for PV Application A. Darwish A. Elserougi, A. S. AbelKhalik S. Ahme A. Massou D. Holliay, B. W. Williams University of Strathclye, UK Alexanria University, Egypt Texas A&M university at Qatar Qatar university University of Strathclye, UK Abstract This paper presents a new threephase cac inverter base on the basic uk converter. The main feature of the propose topology is the fact that the energy storage elements as inuctors an capacitors values can be reuce in orer to improve the reliability, reuce the size, an the total cost. Moreover, the buckingboosting inherent nature of the uk converter, epening on the varying uty ratios, provies more flexibility for stanalone an gri connecte applications when the reuire output A voltage is lower or greater than the D sie voltage. This property is not foun in the conventional current source inverter (SI) when the D input current is always greater than the ac output one or in the conventional voltage source inverter (VSI) as the output ac voltage is always lower than the c input one. Average large an small signal moels are use to stuy the uk nonlinear operation. Basic structure, control esign, an MATLAB/SIMULINK results are presente in this paper. The new threephase DA inverter is very convenient for PV applications where continuous average input currents are reuire for appropriate Maximum power Point Tracking (MPPT) operations. Keywors D/D converters, uk onverter, Buckboost inverter, state space Averaging, control, P control NOMENLATUE eference value of a variable Abc Threephase stationary frame uk converter capacitor uk converter uty ratio D Steay state uk converter uty ratio Direct an uarature synchronous frame E in uk input D voltage f Output voltage funamental freuency f s Sampling freuency I in Total input current I L1 uk converter input current I L2 uk converter output current L 1 an L 2 uk converter input an output inuctors Loa resistance t s Sampling V c uk capacitor voltage V c2a,b an c uk output threephase voltage V o Output loa voltage I. INTODUTION Nowaays, there is an international tren towar moular structure renewable/istribute system concepts in orer to reuce the costs an provie high reliability [1]. This affects the D/A converter topologies significantly in terms of reucing the size an numbers of passive components of the inverter [2]. For conversion between D to A powers, the conventional voltage source inverter (VSI) is the most common converter topology [3]. The instantaneous average output voltage of the VSI is always lower than the input c voltage. For this reason, a boost cc converter shoul be use when the reuire A peak output voltage is greater than the input D voltage [4]. This aitional boost cc converter can result in high volume, weigh, cost, an losses []. In [3], a new inverter is presente as a boost inverter where the reuire output voltage can be lower or greater than the input c voltage by connecting the loa ifferentially across two c c converters an moulating the c c converter output voltages sinusoially. In this topology, both iniviual boosts are riven by two 18 phaseshifte cbiase sinusoial references. The ifferential connection of the loa leas to cancellation of the D offsets of the output voltage an the peak value of this ac voltage can be lower or greater than the c input voltage. The main rawback of this structure eals with its control as the control of the A output voltage reuires controlling both Boost converters an hence, the loa voltage is controlle inirectly. In [6], a closeloop sinusoial PWMD control metho with real waveform feeback techniues is presente. In [7], the simulation of hybri boost inverter control system is propose in orer to show the D offsets error. The topologies of buck, boost, an buckboost inverter have been presente in [8]. In [9], the boostinverter topology is use to buil a singlephase single power stage Fuel ell system with a backup battery storage unit. Four switches an four ioes are use as well as two output capacitors for each phase. In [1], the authors propose a parallel operation of threephase A to D converter using singlephase rectifier moule. The control strategy has high ynamic features, an it can achieve a fast ynamic transient response. However, the propose configuration inclues six uk converters with six rectifiers, two singleswitch singleioe uk converters with two rectifiers for each phase. This all as to the cost, control complexity an the reliability of the overall system in aition to the use of high value capacitor across the loa. For the moern power conversion applications, continuous input current converters are more attractive solutions for renewable systems. In aition, Maximum Power Point Tracking (MPPT) techniues of Photo Voltaic (PV) systems reuire the input current to flow continuously [11] [14]. Generally, there are nine continuous input an output current cc converters of total 33 DD possible singleswitch an singleioe ccconverter. These nine converters inclue

2 two inuctors an a one capacitor [14]. Among these converters with continuous input current, uk converter has the lowest losses an the best voltage regulation. Moreover, the switche capacitor of uk converter increases the voltage boost ability [14]. Because of their buckboost capability, uk converters are use wiely in inustrial c power supplies such as in win energy, Photovoltaic (PV) systems, marine, lightemitting ioe river, compressors, fuel cells, an batteries [1]. Moreover, the current sourcing nature of uk converter enables for easy parallel connection. This can be a tren for paralleling many PV arrays on the same Point of ommon oupling (P). The DD operation of uk converters is stuie extensively an reporte in the literature. Stability of the open loop an close loop operation is consiere in [16]. Generally, DD converters, incluing the uk, are variant systems. This means that the overall transfer function of the converter escribing the inputoutput performance is epenent on the uty ratio as well as the converter parameters. This increases complexity in the control esign as the poles an zeros of converter travel through a specifie trajectory. Moreover, the varying transfer function leas to a istortion in the output voltage an current [17]. This paper proposes a new threephase D/A Inverter base on three biirectional twoswitch twoioe uk converters without/or with an optional small Dlink capacitor. The D/A inverter is expeient for PV applications where the peaks of the output A currents are reuire to be flexible over an below the input D current for MPPT operation an for proviing an easy paralleling at P. II. SYSTEM DESIPTION The operating moes of a typical uk converter can be shown in Fig. 1. The circuitry consists of an input voltage source E in, two switches S 1 an S 2, two antiparallel ioes D 1 an D 2. The energy between the voltage source an the loa is transferre through capacitor. The energy is store instantaneously in inuctors L 1 an L 2. Where Where, an ii. S 1 ON an S 2 OFF (T off < t < T s ), an (1c) (1) (1e) (2a) (2b) (2c) (2) (2e) Averaging the state space euations all over the perio [<t<t s ] assuming the uty ratio () = (3a) A. uk onverter Moeling Using State Space Averaging metho State space averaging metho will be use to moel the uk converter. Assuming the turn off of S 1 is T off, turn on for S 1 = ON is T on an T s = T on T off, the state space euations uring continuous conuction moe of operation can be written as follows: i. S 1 OFF an S 2 ON ( < t < T off ) Where, an (3b) (3c) (1a) (1b) From 3c, the voltage transfer function of the uk converter can be written as: (3)

3 actual an ref voltages Amplitue Imaginary Axis From 3, it can be notice that the ynamics of output voltage epens on the uty ratio (). At the steay state, ( an when = D is constant, the transfer function tens to: (3e) For the parameters shown in Table I, the poles an zeros of G v are erive an plotte in Fig. 2a in orer to stuy the ynamic behavior. The uty ratio is varie from.1 to.8. It can be conclue that increasing the uty ratio, leas the ominant poles of the real axis to move to the slower region, towars the origin, an the system ynamics become slower. This can be verifie from the step response in Fig. 2b as the system gets slower with increasing the uty ratio. To show the meaning of the previous analysis, a MATLAB simulation is use when the uty ratio is varie accoring to G v to raw a sinusoial output voltage with a D offset. The input voltage is set to 2V. Fig. 2c shows the ifference between the reference an the actual output voltages because of the variation of ynamics with the value of uty ratio. L 1 L 2 f f s Table I. System Parameters 1 mh 1 μf 1 mh 1 Ω Hz KHz The propose threephase D/A inverter base on uk converters is shown in Fig. 3. As a current source, the propose system can be parallele easy for any further power extension. Each uk converter buils a sinusoial output voltage, specifically current, with a Doffset. Because of the balance energy operation of the three phases, it is expecte that the D offsets of each phase are cancelle an the threephase loa expert pure sinusoial voltages an currents. Fig. 4 shows the open loop operation of the system in Fig. 3 with the parameters in Table I an 1 nf optional output shunt capacitors. The expecte output voltages at points V c2a, V c2b an V c2c are sinusoial voltages of magnitue 2V peak an 4V D offset. The uty ratios of the three uk converters, a, b an c are calculate from (3e) an have been shown in Fig. 4a. However, the output voltages in Fig. 4b are istorte. It can be seen clearly from the output currents in the synchronous rotating frame in Fig 4c that a 2 n harmonic appears because of uk nonlinearity. This is because the varying ynamics at each point, which is explaine in Fig. 2. L1 IL1 S1 Vc D1 S2 uk onverter L2 IL2 D2 Vo (c) L1 S 1 = OFF, L 1 ischarges, charges an L 2 ischarges L1 Vc L2 S 1 = ON, L 1 charges, ischarges an L 2 charges Fig. 1 The operating moes of a typical uk converter Poles an zeros of G v Step esponse of G v (c) uk with varying uty ratio Fig. 2 Freuency an analysis of uk onverter In the next section, a control strategy is propose for the uk inverter system in orer to eal with the nonlinearity, control the esire output current, an eliminate the preefine istortion. III. ONTOL DESIGN The control objective is to track a preefine sinusoial output voltage. The control structure for the converters is shown in Fig.. V, V an V c are the irect, uarature, an D offset components of the output voltage at V c2a, V c2b an V c2c. Vc 1 x 14 PoleZero Map D1 =.1 D2 =.3 D3 =.. D4 =.7 D = eal Axis Step esponse L2 D1 =.1 D2 =.3 D3 =. D4 =.7 D =.8 Vo Vo Time (sec) Actual ef

4 Output urrent (A) Output urrent (A) Inverter threephase uty ratios PV Iin IL1c uk 3 Vc2c Fig. 3. Propose uk base D/A threephase Inverter.6.6 IL1a IL1b uk 1 uk 2 b a b c a c constant over a long perio, epening on the MPPT operation, an hence the control input shoul be written in terms of the varying uty ration. The small signal euations of the uk converter can be riven from euation 3c by consiering the small signal eviations. where;, an are the steay state values of, an (4a) (4b) Duty ratios Vc2c Output voltages at V c2a, V c2b an V c2c (c) Output currents (threephase an components) Fig. 4. Open loop operation of the propose system in Fig. 3. The subscript is referre to a reference value. K p an K i are the proportional an integral gains of the controller. The etaile mathematical analysis of the nonlinear uk converter is out scope of this paper an will be consiere in further publication. From euation 3b, the control input is consiere as the input voltage E in. However, normally, the voltage of the PV is where; an are the steay state values of respectively In orer to ease the control esign process, a point at the mile of the trajectory in Fig. 3a, where =., is chosen to be an intermeiate operating point. The poles loci of the close loop system of E. (4b) are plotte in two ifferent ways. In Fig. 6a, K i is hel constant at (.7) an K p is varie in the range [.1:.8]. In the same way, Fig. 6b shows when K p is hel constant an K i varies from [.1:.8]. From Fig. 6a, it can be notice that increasing the proportional value will rive the poles towar the right han sie. An from Fig. 6b, the imaginary poles are stuck in their loci while the real poles move away from the origin to the left han sie. The gain values are selecte by compromising between the both cases. From Fig. 6a an b, selecting the values of K p =.3 an K i =.4 provies preliminary proper ynamic performance an stability margin from the imaginary axis. IV. SIMULATION ESULTS The propose threephase uk inverter is simulate in MATLAB/SIMULINK with the selecte parameters an gain values. Fig. 7 shows the results for the voltage response. The output voltages are shown in Fig. 7a with 4V D offset an 2V peaktopeak. However the components in Fig. 7b show that the actual output voltages an currents have secon harmonic components. This can be explaine by the nonlinear nature of the uk converters as escribe in the previous section. By increasing the parameters of the uk onverters (L 1, L 2 an ), the trajectory of the poles in Fig. 2a becomes shorter. Hence, the effect of uk nonlinearity becomes less an the 2 n orer harmonic will ecrease in the output currents an voltages. However, increasing the converter parameters will affect the size, cost, losses an will a to the control complexity. As a solution, the controller is moifie as in Fig. 8. A ban pass filter tune at the 2 n harmonic, 3 r harmonic from the frame point of view, to extract its components in the output voltage.

5 Imaginary Axis Output urrents (A) Imaginary Axis Output voltage D offset (V),b,c o a c b Output voltages at V c2a, V c2b an V c2c an corresponing components 2 c c Fig. ontrol Structure PoleZero Map (Ki [.7] & Kp = [.1:.1:.8] corresponing components of voltages at V c2a, V c2b an V c2c eal Axis Polezero map of (4b) when K i is hel constant at (.7) an K p is varie in [.1:.8]. Polezero map of (4b) when K p is hel constant at (.1) an K i is varie in [.1:.8]. Fig. 6. oot loci for a fixe K i an a range of K p or vice versa. A proportionalresonant (P) controller is inserte to force this component to zero. The values of P controller are chosen to be very small as they o not interrupt the main loop. The results are shown in Fig. 9 where the P controller is able to suppress the 2 n harmonic components from the voltages an currents. Fig. 1 shows the experimental results for Fig.9 using TMS32F2833 DSP. AKNOWLEDGMENT Kp =.1 Kp =.2 Kp =.3 Kp =.4 Kp =. Kp =.6 Kp =.7 Kp =.8 PoleZero Map (Kp =[.7] & Ki = [.1:.1:.8] Ki =.1 Ki =.2 Ki =.3 Ki =.4 Ki =. Ki =.6 Ki =.7 Ki = eal Axis This publication was mae possible by NPP grant (NPP ) from the Qatar National esearch Fun (a member of Qatar Founation). The statements mae herein are solely the responsibility of the authors (c) Output voltage D offset () Output urrents Fig. 7 The propose system uner control V. ONLUSION Due to its inherent current sourcing nature, uk converter is consiere as an attractive alternative for the conventional cac converters in PV applications. The reason for that is the continuous input current, which enables for irect MPPT techniues, an the ability of paralleling more than cac converter at the same P. Moreover, because of the small input current ripples, no capacitor is reuire across the PV array or even use; it s a small plastic capacitor instea of electrolytic one. In this paper, a threephase DA uk converter base current source inverter has been propose an stuie. The state space averaging metho was use to esign the control structure. The uk converter inherent nonlinearity is a main reason for output currents an voltages istortion. The effect of this nonlinearity can be relieve by increasing the uk converter inuctors an capacitors values. However, this will affect the total cost, size an control complexity. In this work, an aitional control loop is propose to reuce the istortions with the minimal passive element values. Satisfactory results in terms of reuce 2 n orer harmonic components in the output currents an voltages were obtaine an verifie by MATLAB/SIMULINK.

6 ,b,c Output urrents (V) Output urrents (A) Output voltage D offset (V) c BP 3 r harmonic c Fig. 8 ontrol structure with eliminating the 3 r harmonic in the frame (2 n in the stationary) Output voltages at V c2a, V c2b an V c2c an corresponing components P P o Output voltage D offset (c) Output urrents an corresponing components Fig. 9 The propose system uner P control Vc2c a b c Voltages at V c2a, V c2b an V c2c Loa Voltages Fig. 1 Experimental esults EFEENES [1] Johanna M.A. Myrzlk, " Novel Inverter Topologies for Singlephase StanAlone or Grionnecte Photovoltaic Systems," IEEE PEDS 21 Inonesia, vol. 1, no. 1, pp , Oct 21. [2] W. Kleinkauf, J. Sachau, H. Hempel: Developkts in inverters for photovoltaic systems Moular power conitioning an plant technology,1 Ith E.. Photovoltaic Solar Energy onference, Montreux, [3] am on O. aceres an an Ivo Barbi, A Boost D A onverter: Analysis, Design, an Experimentation," IEEE Trans. on Power Electronics, vol. 14, no. 1, pp , Jan [4] F. Barzegar an S. uk, Solistate rives for inuction motors: Early technology to current research, in Proc. IEEE egion 6 onf., Anaheim, A, Feb. 1 18, [] S. B. Kjær, J. K. Peersen, an F. Blaabjerg, A review of singlephase griconnecte inverters for photovoltaic moules, IEEE Trans. In. Appl., vol. 41, no., pp , Sep./Oct. 2. [6] Yaosuo Xue an Liuchen hang, loseloop SPWM ontrol for Grionnecte BuckBoost Inverters, 24 3 th Annul IEEE Power Electronics Specialists onference, vol., no., pp , June. 24. [7] T. D. achmilha, Y. Haroen, A. Muorobin, an E. ijanto Single Phase Boost Inverter Using Hybri Moelling Approach, IEEE onference on Power Engineering an enewable Energy 212, pp. 1 6, Jul [8] B. Prasa, S. Jain, an V. Agarwal, Universal SingleStage Gri onnecte Inverter, IEEE Trans. Energy onversion., vol. 23, no. 1, pp , March. 28. [9] M. Jang, M. iobotaru, an V.G. Ageliis, A SinglePhase Gri onnecte Fuel ell System Base on a BoostInverter, IEEE Trans. Power Electronics. Appl., vol. 28, no. 1, pp , Jan [1] V. hunkag an U. Kamnarn, Parallelling threephase A to D converter using UK rectifier moules base on power balance control techniue, IET Power Electron., 29, vol. 3, no.4, pp [11] Y. Xue, L. hang, S. B. Kjær, J. Boronau, an T. Shimizu, Topologies of singlephase inverters for small istribute power generators: An overview, IEEE Trans. Power Electron., vol. 19, no., pp , Sep. 24. [12] L. Quan an P. Wolfs, A review of the single phase photovoltaic moule integrate converter topologies with three ifferent D link configurations, IEEE Trans. Power Electron., vol. 23, no. 3, pp , May 28. [13] J. M. A.Myrzik anm. alais, String anmoule integrate inverters for singlephase gri connecte photovoltaic systems A review, in Proc. IEEE Bologna Power Tech onf., Jun , 23, vol. 2, p. 8. [14] B. W. Williams, DtoD onverters With ontinuous Input an Output Power, IEEE Trans. Power Electron., vol. 28, no., pp , May [1] H. S. H. hung, K. K. Tse, S. Y.. Hui,. M. Mok, an M. T. Ho, A novel maximum power point tracking techniue for solar panels using a SE or uk converter, IEEE Trans. Power Electron., vol. 18, no. 3, pp , May 23. [16] F. A. Himmelstoss an. M. Walter, A simple uk converter erivate twouarant D motor controller, in Proc. Int. Symp. Power Electron. Electr. Drives Autom. Motion, Jun. 21, pp [17] J. Mahavi, A. Emai, an H.A. Toliyat, Application of State Space Averaging Metho to Sliing Moe ontrol of PWM D/D onverters., IEEE Inustry Applications Society Annual Meeting New Orleans, Louisiana vol. 2, no. 2, pp , Oct