A Novel Sine Duty-Cycle Modulation Control Scheme for Photovoltaic Single-Phase Power Inverters

Transcription

1 Leandre Nnee Nnee, Jean Mbihi A Novel Sine Duty-Cycle Modulation Control Schee for Photovoltaic Single-Phase Power Inverters ARNAUD OBONO BIYOBO Research Laboratory of Coputer Science Engineering and Autoation ENSET, University of Douala Po. Box 872, Douala, CAMEROON obonobiyo@yahoo.fr LEANDRE NNEME NNEME Research Laboratory of Coputer Science Engineering and Autoation ENSET, University of Douala Po. Box 872, Douala, CAMEROON leandren@gail.co JEAN MBIHI bihidr@yahoo.fr, Research Laboratory of Coputer Science Engineering and Autoation ENSET, University of Douala Po. Box 872, Douala, CAMEROON Abstract: - In this paper, a novel SDCM (sine duty-cycle odulation) schee for photovoltaic (PV) singlephase power inverter is presented. Unlike popular SPWM (sine pulse width odulation) strategies, the SDCM control schee consists of a iniu nuber or building coponents, while offering a robust feedback control topology. The ain DC power to be converted, is delivered by an upstrea PV panel. Then, a SDCM circuit with appropriate basic odulation frequency, is used as a switching driver for power MOSFETs of a single phase H-bridge inverter. The erits of the proposed SDCM control schee, are proven using analytical developents, followed by relevant virtual siulations conducted on a prototyping power inverter within Multisi software fraework. Moreover, the virtual siulation results obtained are presented, in order to show the high quality of the proposed class of SDCM control schees for PV Single-phase power inverters. Key-Words: - Sine duty-cycle odulation, control schee, open-loop control, photovoltaic, single-phase, power inverters, LC filter, virtual siulation. Introduction A power inverter is a controlled interfacing systes, between a ain DC energy source and an AC load to be supplied. Although power inverters are widely encountered in industrial electronics for a wide variety of technical applications, they are increasingly used nowadays in solar power systes [-3]. A nuber of research works have been published so far on single-phase PV (photovoltaic) inverters [4-7]. However, in ost of these pioneering works, the great ephasis is on the iproveent or extension of existing SPWM (sine pulse width odulation) control strategy for PV-based energy systes. Moreover, according to a few available recent scientific papers, any weaknesses are hidden behind the basic PWM (pulse width odulation) principle, e.g., coplexity of triangle odulation clock, open-loop control topology, constant odulation frequency and ore. E-ISSN: X 05 Volue 7, 208

2 Leandre Nnee Nnee, Jean Mbihi The originality of this research paper is to study a novel high frequency switching odulation topology for single-phase power inverters for singlephase AC loads. It is founded on a siple DCM (duty-cycle odulation) strategy, initiated earlier since 2005 [8] for industrial instruentation purpose. Over years, it has been increasingly used further as a versatile odulation technique, for solving a wide variety of instruentation probles, including ADC (analog-to-digital conversion)[9]- [0], DAC (digital-to-analog conversion) [-3], and analog signal transission [4-6]. However, according to our best knowledge, the first recent applications of DCM control schees in power electronics is restricted to the class of DC-DC power converters, e.g., Buck converters [7], Boost converters [8] and new digital odulation drivers [9]. Therefore, the novelty of this paper is to show fro analytical developents and virtual siulation basis, that unlike popular SPWM (sine pulse width odulation) strategies with hidden relevant weaknesses, the proposed novel SDCM (sine dutycycle odulating) control schee, offers iniu hardware siplicity, lower ipleentation costs, attractive odulation properties and quality for PV-based single-phase inverters. In section 2 of this paper, the SDCM principle is outlined. Then, the SDCM control schee for PVbased single-phase inverters is detailed in section 3. Furtherore, in section 3, virtual siulations is conducted on a prototyping power inverter syste and the relevant results obtained and related findings are presented, followed by the conclusion of the paper in section 4. 2 Principle of SDCM Strategy The SDCM strategy recalled in this section is a signal processing technique, allowing to transfor a sine wave input u(t) = a sin(2π f s t + θ) into a switching odulated wave u (x(t)) u (t) with tie varying pulse width T on(u(t)) T on(t) and period T (u(t)) T (t). In that case, the odulating input can be recovered fro the DCM function R (x(t)) R(t) where R (t) = T on(t)/t (t). Although the SDCM principle sees apparently intricate, it is fortunately surprising to discover as shown in Fig. that, copared to a basic PWM circuit (Fig. (a)), a DCM circuit (Fig. (a) however relies on iniu building coponents. Indeed, it consists of a single integrated operational aplifier, associated with four passive coponents with design paraeters R, R2, R3 and C respectively. Fig. SPWM (a) and SDCM (b) circuits Fro Fig. (b), it is iportant to recall that the Fourier s series of the tie varying periodic T (u(t)) T (t) of the SDCM wave, could be written as follows ([-5]): u ( u( t)) u ( t) = C ( u( t)) where, 0 t + Cn ( u( t)) cos 2π n () n= T ( u ( t )) ( ) 4Vcc sin ( nπ R ( u( t)) ) C0 ( u( t)) = 2 R ( u( t)) Vcc Cn ( u( t)) =, n π n R ( u( t)) α2u( t) ( + α) Vcc ln T ( u( t)) α u( t) + ( α ) Vcc T ( u( t)) ( α2u( t) ) (( + α) Vcc) ln 2 2 ( α2u( t) ) ( ( α ) Vcc) on 2 = = 2 2 (2) (3) E-ISSN: X 06 Volue 7, 208

3 Leandre Nnee Nnee, Jean Mbihi Fig. 2 Spectra of PWM and DCM waves for the sae basic odulation frequency It is iportant to outline the fact that for a SPWM strategy, the odulation period T in () is a pure constant paraeter, while R (u(t)) in (2) is a linear function of u(t) since Ton(u(t)) and T off (u(t)) = T- T on(u(t)) are linear over the involved odulating space. Moreover, although (3) is apparently a dreadful nonlinear function, it has been shown that it is rigorously linear in a wide vicinity of the rating point (R =0, u=/2). Therefore, the linear expression obtained fro the first order Taylor series of (3) is given by, Rɶ ( x( u( t) = pu( t) +, where 2 α V c c ( + α ) p = (4) + α lo g α Moreover, the basic odulation period for u (t) = 0 is given by : + α R T (0) 2 R C log = 3 where α = α (5) R + R 2 As an illustrative exaple, given the following set of data {Vcc = 2 V, R= 0k, R2= 8.2k, R = 0k, C = 2 nf }, the resulting graphs obtained for { R ( ( )) u t, Rɶ ( u( t)), PWM and DCM spectra}, and presented in Fig. 2. Fig. 2() shows that the linear approxiation Rɶ (( u( t)) is exactly closed to R ( ( )) u t in a wide range estiated to [-7 volts, 7 volts], with p = in (4) and {α = , T (0) = /20.24 khz} in (). In addition, as shown in Fig. 2(b) where the graphs of noralized PWM and DCM spectra are presented, it is clear that the PWM strategy with constant frequency f pw(0) = /T (0)), offers a greedy frequency spectru copared to that of the DCM strategy. Moreover, another relevant finding eerging fro Fig. 2(b) is that, the aplitude of DCM haronics with rank ultiple of 3 are null. That fact ight be a erit for reducing stresses on power MOSFETs of the H- bridge inverter, while iproving the quality of the AC load voltage downstrea the power LC filter. As a straightforward iplication, the DCM wave u (u(t)) defined by ()-(2), indicates that a odulating sine input given by u(t) = a sin(2π f s t + θ) could be recovered fro the DCM odulated wave u (u(t)) with an eroded haronic spectru, using an appropriate linear low-pass filter with gain given as follows : (+ α ) + α k = 2pVcc = l og (6) 2α α The palette of Equations ()-(6) stands for the analytical deonstration of the SDCM principle used in this paper, as a novel building strategy for single-phase PV power inverters with pure sine output voltage. E-ISSN: X 07 Volue 7, 208

4 Leandre Nnee Nnee, Jean Mbihi 3 SDCM Control Schee for Single Phase Power Inverter The scheatic diagra of the proposed SDCM control schee for PV single-phase power inverters is presented in Fig. 3. The power electronics topology is not new and consists of a solar ediu, a PV panel with E = 2 x 2 (volts), a single phase H-bridge MOSFET inverter, a downstrea low-pass filter, and an AC Fig. 3 SDCM schee for single-phase PV power inverters load to be supplied. Moreover, the four gates of power MOSFET switches are controlled fro a sine odulating voltage u(t) = a sin(2π f s t + θ), via a novel SDCM circuit described in the previous section. Viewed fro the SDCM output signal u (x(t)), the H-bridge MOSFET inverter exactly behaves under the sun lighting ediu as a power aplifier with ideal static gain E/Vcc, whiles the resulting power odulated wave U (x(t)) has the sae wavefor and periodicity paraeters (pulse width T on(x(t)), period T (x(t)) than u (x(t)). In this case, the odel of the switching power voltage delivered by the H-bridge MOSFET inverter, coputed fro ()-(3) given that R(Us(t)) is dictated by R(x(t)), i.e., R(Us(t)) = R(x(t)), is given as follows : U ( u( t)) U ( t) = A ( u( t)) + 0 t An ( u( t)) cos 2π n (7) n= T ( u ( t )) where, ( ) 4 E sin ( nπ R ( u( t)) ) A0 ( u( t)) = 2 R ( u( t)) E An ( u( t)) =, n (8) π n with, Rɶ ( x( u( t) = pu( t) + (9) 2 where, α V c c ( + α ) p = (0) + α lo g α Because of the siilarity of ()-(2) and (7)-(8), and according to the SDCM principle, the power iage Us(t) of the odulating input u(t) encapsulated in U (x(t)), can be recovered upstrea the AC load to be supplied, using a suitable low-pass LC filter with static gain depending on a given supplying AC voltage required by the load. 4 Case Study of an SDCM Control Schee for PV Power Converter The virtual odel of the prototyping SDCM control schee for PV single-phase power inverters in presented in Fig. 3. The nubers of building parts are (Main DC power supply fro PV panel), 2 (H-bridge IRF840 MOSFET inverter), 3 (low-pass LC filter), 4 (load with terinal power resistance Ro = 250Ω ), 5 (Vcc voltage source), 6 (low frequency signal source for u(t) = 4 sin(2π 50 t + θ) volts, 7 (SDCM circuit), 8 (logic conforer), 9 (Virtual oscilloscope for the easureents of u(t) and u (u(t)) waves) and 0 (virtual oscilloscope for the easureent of u(t) and the related response Us(t) at the load terinals. Recall that the SDCM circuit used in Fig. 4 is the sae as that presented earlier in the illustrative exaple (see Fig. 2)), where f (0) = /T (0) = khz. Recall also that Ua-Ub in Fig. 4 is equal to the power switching input voltage U(u(t)) of the low-pass LC filter. Moreover, the transfer function of that LC filter is given as follows: Us( s) F( s) = = () U s 2 ( ) L C s + R C s+ The bode diagra of the LC filter obtained under Matlab fraework using R = 200 H, L = 50 H, C = 66uF is presented in Fig. 5. It is iportant to observe that the odulating frequency of 50 Hz required by the terinal AC load lies within the pass-band of the low-pass filter, and the basic odulation frequency f (0) = khz is so far fro 50 Hz that it should be cut off copletely. As an iplication, the predicted load voltage Us(t) will be absolutely a pure sine wave. E-ISSN: X 08 Volue 7, 208

5 Leandre Nnee Nnee, Jean Mbihi Fig. 4 Virtual odel of prototyping SDCM control Schee for PV single-phase power inverter Fig. 5 Bode diagras of the low-pass LC filter The odulating and odulated signals of the SDCM circuit obtained when siulating the prototyping virtual SDCM power inverter syste, are presented in Fig. 6, where the aplitude of u (t) is a = 4 volts and the switching threshold levels of x(t) are ±Vcc = ±2 V. E-ISSN: X 09 Volue 7, 208

6 Leandre Nnee Nnee, Jean Mbihi Fig. 6 Shape of signals u(t) and u(x(t)) of the SDCM driver Fig. 7 Shapes of the odulation signal u(t) and the power voltage Us(t) for (Ro = 250 Ω) In addition, Fig. 6 shows the shapes of the odulating signal u(t) and the power voltage u (t), whereas in Fig. 7, u(t) and the predicted voltage Us(t) delivered to the load is a pure AC sine voltage, with basic frequency fs = 50 Hz, and stable aplitude a =.5 volts which can be shifted freely if needed, using an appropriate power transforer (see Fig. 4). E-ISSN: X 0 Volue 7, 208

7 Leandre Nnee Nnee, Jean Mbihi Fig. 8 Shapes of the odulation signal u(t) and the power voltage Us(t) for (Ro = 50 Ω) Fig. 9 Shapes of the odulation signal u(t) and the power voltage Us(t) for (Ro = 350 Ω) E-ISSN: X Volue 7, 208

8 Leandre Nnee Nnee, Jean Mbihi Before to conclude this paper, it is also iportant to point out the fact that the well tested novel SDCM control schee presented in this research work, is an open loop control schee. As a consequence, disturbances due to load changes ight lead to significant variations of the supplied voltage Us(t) as shown in Fig. 8 for higher power deand, e.g., Ro = 50 Ω. Moreover, as presented in Fig. 9, a lower power deand, e.g;, Ro = 350 Ω, ight also leads to an unpredictable increase in the load voltage Us(t). In all cases, the undesired effects of unpredictable disturbances, even poor static and dynaic perforances, are the coon weaknesses of all open-loop dynaic control systes. Such intricate phenoena can be satisfactory cancelled using standard feedback control strategies available in autoatic feedback control practise. 5 Conclusion The novelty of the SDCM control principle presented in this paper for single phase PV power inverters has been proven, using analytical developents as well as coputer-aided siulations of a well tested virtual syste. In future research works, it would be interesting to transfor the virtual reality study into realistic ipleentation. In would be appreciable also to overcoe the weaknesses of open-loop controls by robust feedback control strategies. ACKNOWLEDGEMENTS The authors of this research works wishes to acknowledge the great relevant effects of the scientific research grant offered by the Ministry of Higher Education of Caeroon. It has facilitated the access to support and technical research resources needed for ost editing activities involved in this research work REFERENCES [] B. M. Shara, New Trends in Solar Energy Modeling and Developing a Relation for Perforance of Solar Radiation, European Jurnal of Advances in Engineering and Technology, 207, 4(9), [2] H. Koran, T. LaBella and J-S. Lai, High Efficiency Photovoltaic Source Siulator with Fast Response Tie for Solar Power Conditioning Systes Evaluation, IEEE Transactions on Power Electronics, 204, 29 (3), [3] R Wai and W Wang, Grid-Connected Photovoltaic Generation Syste, IEEE Transaction on Circuits and Sys-tes, 2008, 55 (3), [4] A.A Hassan, F. Fay, A. E.A Nafeh, M. A. and El-Sayyed, Modelling and Siulation of a single phase grid connected photovoltaic syste, Wseas Transactions on Systes and Control, January 200, (5), [5] M. Dave and S. R. Vyas, Siulation and odelling of single phase DC-AC converter for solar inverter, International Research Journal of Engineering and Technology, Deceber 205, 02(9), pp [6] S. M. Cherati, N. A. Azili, M. Ayob and A. Mortezaei, Design of a current ode PI controller for a single phase PWM Inverter, IEEE Applied Power Electronics Colloqui, 20, pp [7] K. G. Gosni and G. GhoshZhan,Closed loop PI design of single-phase otor using SPWM, International Journal of Advances Research in Coputer Science and Software Engineering, 207, 7(6), pp [8] Mbihi, B. Ndjali and M. Mbouenda, Modelling and Siulation of a Class of Duty-Cycle odulators for Industrial Instruentation, Iranian Journal of Electrical and Coputer Engineering, 2005, 4(2), pp [9] Mbihi, B. Ndjali and M. Mbouenda, A novel Analog-To-Digital Conversion Technique Using Duty-Cycle Modulation, International Journal of Electronics and Coputer Science Engineering, 202, (3), pp [0] J. Mbihi and L. Nnee Nnee, A Multi- Channel Analog-To-Digital Conversion Technique Using Parallel Duty-Cycle Modulation, International Journal of Electronics and Coputer Science Engineering, 202, (3), pp [] Moffo Lonla B., Mbihi J., Nnee Nnee L., Ko M., A Novel Digital to Analog Conversion Technique using Duty-Cycle Modulation, International Journal of Circuits, Systes and Signal processing, 203. [2] B. Moffo Lonla. And J. Mbihi, A Novel Digital Duty Cycle Modulation Schee for FPGA- Based Digital-to-Analog Conversion, IEEE Transaction on circuits and syste II, 205, 62(6), pp [3] B. Moffo Lonla, J. Mbihi and L. Nnee Nnee, FPGA-Based Multichannel Digital Dutycycle Modulation and application to siultaneous Generation of Analog Signals, STM Journal of Electronic Design Technology (JoEDT), 207, 8(), pp [4] L. Nnee Nnee, J. Mbihi, Modeling and Siulation of a New Duty Cycle Modulation E-ISSN: X 2 Volue 7, 208

9 Leandre Nnee Nnee, Jean Mbihi Schee for Signal Transission Syste, Aerican Journal of Electrical and Electronic Engineering, 204, 2(3), pp [5] Moffo Lonla B., Jean Mbihi, Leandre Nnee Nnee. A Low Cost and High Quality Duty Cycle Modulation Schee and Applications. International Journal of Electrical, Electronic Science and Engineering, 204, 8(3), pp [6] Mbihi, Nnee, Ko, A Suboptial Nonlinear Duty-cycle Modulation Schee, STM Journal of electronic Design Technology, 206, 7(), pp [7] J. Mbihi and L. Nnee Nnee, A Novel Control Schee for Buck Power Converters using Duty Cycle Modulation. International Journal of Power Electronics, 203, 5(3/4), pp [8] Y. P. Danwé Sounsouou, H. Djalo, J. Mbihi, et J. Y. Effa, Modelisation Virtuelle d un nouveau schea de réglage de Boost à coande rapprochée par odulation en rapport cyclique, Journal Afrique Science, 3(), 207, pp [9] J. Mbihi, Dynaic odelling and virtual siulation of duty-cycle odulation control drivers, International Journal of Electrical, Electronic Science and Engineering, 207, (4), pp E-ISSN: X 3 Volue 7, 208