HIGH EFFICIENCY GRID TIED INTERLEAVED FLYBACK MICRO INVERTER WITH HYBRID MODE FOR PV AC MODULES 1 VODDINENI SHASHI KUMAR, 2 A.

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1 HIGH EFFICIENCY GRID TIED INTERLEAVED FLYBACK MICRO INVERTER WITH HYBRID MODE FOR PV AC MODULES 1 VODDINENI SHASHI KUMAR, 2 A. NARASIMHA RAO 1 M.Tech, VIDYA JYOTHI INSTITUTE OF TECHNOLOGY, Affiliated to JNTUH, Hyderabad, Telangana, India. 2 Associate Professor, VIDYA JYOTHI INSTITUTE OF TECHNOLOGY, Affiliated to JNTUH, Hyderabad, Telangana, India. ABSTRACT- Boundary Conduction Mode (BCM) and Discontinuous Conduction Mode (DCM) control strategies are widely used for the flyback micro inverter. For the interleaved flyback micro inverter, the dominant losses with heavy load include the conduction loss of the power MOSFETs and diodes and the loss of the transformer while the dominant losses with light load include the gate driving loss, the turn off loss of the power MOSFETs and the transformer core loss. Based on the loss analysis, a new hybrid control strategy combining the two-phase DCM and one-phase DCM control is proposed to improve the efficiency in wide load range by reducing the dominant losses depending on the load current. The proposed control strategy consists of two components: the proportional-resonant (PR) controller with the harmonic compensator (HC) and the hybrid nominal duty ratio. Moreover, by applying the hybrid nominal duty ratio yielded from the proposed operation mode selection, the disturbance rejection is achieved more effectively, and the control burden is reduced. Finally, the simulation results were shown to verify the tracking speed and disturbance rejection performances of the proposed control strategy. I. INTRODUCTION The interest in exploring renewable energies has grown in the last years due to the energy crisis. Photovoltaic (PV) sources are predicted to have the highest increase 30% in the next decade and to be the biggest contributor on the electricity generation in 2040 [1]. A PV AC module, which is also called the micro-inverter, is becoming more and more popular and the power range is normally up to about 200 W. With the rapid development of the market, a lot of research work has been done with the topologies and control methods of the microinverters. A modulated boost stage is used to generate a rectified sinusoidal waveform and a Current Source Inverter (CSI) is used to unfold the rectified waveform into the grid [2]-[5]. These topologies usually achieve high efficiency under heavy load, but low efficiency under light load (no more than 90% as reported). Moreover, the complexity and additional components of the above topologies also result in high cost and low power density as a PV AC module. Alternatively, the micro-inverter derived from the flyback converter, named as the flyback inverter, is widely used due to its simple structure, lower cost and higher efficiency [6]. A single stage flyback inverter with the center-tapped secondary winding was presented in [7]-[10]. Each of the secondary winding transfers the energy to the AC side during a half line period with two additional MOSFETs. A modulated flyback DC/DC converter followed by a CSI was presented in [11]-[12]. The SCRs are used in the unfolding stage to reduce the cost and conduction loss. To further improve the efficiency, a soft-switching interleaved flyback micro-inverter. under BCM was presented in [13]. Active clamp and synchronous rectifier technology were adopted in [14]-[16]. But additional auxiliary circuit components are required and this results in higher cost, lower power density and complex control as a PV AC module. The BCM and DCM modulation were used simultaneously during a half line period, because BCM is more suitable to high power levels and DCM is better for low power levels as far as the efficiency is concerned. Owing to the combined control strategy, higher efficiency can be achieved over the conventional BCM control method without additional cost. The reference signal design with the similar control strategy for the single flyback converter with a CSI was proposed in [17]. In this paper, the BCM and DCM control strategies are investigated of the interleaved flyback micro-inverter concentrating on the loss analysis under different load condition respectively. It is noted that the DCM control strategy achieves higher efficiency over BCM for the application of the interleaved flyback micro-inverter within the power range of 200 W. The advantages of two-phase DCM operation are the current sharing and the reduction of the current stress between two interleaved phases so that the conduction loss and turn off loss of the power MOSFETs and diodes as well as the copper loss of the transformer can be reduced with higher output power. On the other hand, the advantage of onephase DCM operation is the reduction of the transformer core loss, the driving loss of the power

2 MOSFETs with lower output power. Since the output power is a pulsating power following a squared sine wave, the idea here is to combine two-phase DCM modulation and one-phase DCM modulation simultaneously according to different output power during a half line period, so that the dominant losses can be optimized and high efficiency is achieved in wide load range In this paper, the current control strategy of the flyback micro inverter with hybrid mode is proposed. The proposed control strategy consists of two components: the PR controller with HC and the hybrid nominal duty ratio. The PR controller with HC provides high gain at the fundamental and harmonic frequencies of the grid and achieves the zero-tracking error in both operation modes. The hybrid nominal duty ratio performs as a feed forward control input and is determined by the proposed operation mode selection. By applying the hybrid nominal duty ratio according to proper operation region, it can achieve more effective disturbance rejection and faster dynamic. Actually, the PV inverter called as the BCM flyback inverter has both operation modes; it inevitably operates in DCM at the low instantaneous power level or low solar irradiation level although it operates in BCM at all instantaneous power levels for rated average power. The system gain of the flyback inverter in the DCM region is inherently much low. To achieve fast reference tracking and disturbance rejection performances, the high gain feed-back controller is required in the DCM operation. Section II presents the analysis of the interleaved flyback micro-inverter under BCM and DCM. Section III presents the proposed control method and its principle of operation. Section IV presents the system design. The simulation results are also provided in Section V. Section VI provides a brief conclusion. II. ANALYSIS OF INTERLEAVED FLYBACK INVERTER UNDER BCM AND DCM A. Topology of the Interleaved Flyback Micro-Inverter Fig.1 shows the main circuit of the interleaved flyback inverter. The inverter comprises of two-phase interleaved flyback converters and a CSI. S1 and S2 are the main power switches; D1 and D2 are the rectifier diodes; NP1 and NP2 are the primary windings, and NS1 and NS2 are the secondary windings. S3-S6 form the CSI to unfold the rectified sinusoidal waveform into the grid. S3 and S6 turn on during the positive half grid period, while S4 and S5 turn on during the negative half grid period. Fig.2 shows the current waveforms of the interleaved flyback inverter. Each phase is 180 phase-shifted in one switching period to achieve ripple cancellation. Thus a lower output filter inductance can be used. Fig.1 Interleaved flyback inverter Fig.2 Current waveforms of the interleaved flyback inverter B. Comparison of BCM and DCM Fig.3 shows key waveforms of the interleaved flyback micro-inverter under BCM and DCM respectively. Under DCM, a constant switching frequency (CSF) control is applied. A variable switching frequency (VSF) is applied under BCM to achieve a sinusoidal output current waveform. It is noticed that the output current frequency is twice of the switching frequency, which leads to the output filter inductance reduction and higher power density can be achieved. The dominant losses with heavy load include the conduction loss of the MOSFETs and diodes, and the core loss and copper loss of the transformer, while the dominant losses with light load include the driving loss, turn-off loss of the MOSFETs and the transformer core loss. The range of the switching frequency increases dramatically as the power level decreases for the flyback microinverter under BCM.

3 Table II. Comparison of BCM and DCM Fig.3 Key waveforms of the interleaved flyback inverter under BCM and DCM For the micro-inverter with two phases, the switching frequency range varies from 113 KHz to 480 KHz under BCM at the power level of 200 W [23]. This causes the driving loss and turn-off of the MOSFETs to increase significantly. Therefore, the efficiency under BCM is much lower than DCM under light load condition. Table I shows the loss distribution comparison under BCM and DCM under half load condition. The specifications are as follows: input voltage: Vdc=36~60 V; grid voltage: Vg=220 VAC; grid frequency: fgrid=50 Hz; switching frequency: fs=100 khz. The components of the power train are as follows: the transformer: Lp=28 μh, Ls=112 μh; S1 and S2: SPW52N50C3 (560 V/52 A from Infineon); D1 and D2: IDP12E120 (1200 V/12 A from Infineon); S3-S6: S8016N (800 V/16 A from Teccor). Table I. Estimated loss distribution under BCM and DCM for the micro-inverter with two-phase operation III. PROPOSED METHOD AND PRICIPLE OF OPERATION A. Loss Analysis of DCM Table III shows the calculated loss distribution of a 200 W interleaved flyback inverter under 100% and 25% load respectively. It is observed that the dominant losses with heavy load include the conduction loss of the power MOSFETs Pmos and diodes Pdiode, the transformer core loss Pcore and copper loss Pcu, whereas the dominant losses with light load include the gate driving loss Pdrive, the turn-off loss Poff of the power MOSFETs and the transformer core loss Pcore. Therefore, minimizing the dominant losses according to load condition is an effective way to optimize the efficiency in wide load range. Table III. Estimated loss distribution of DCM under different load condition for the micro-inverter with two phase operation Fig.4 shows the calculated efficiency of the interleaved flyback micro-inverter under DCM and BCM respectively. A comparison of the microinverter under BCM and DCM is shown in Table II. Based on the above analysis, it should be pointed that for the application of the interleaved flyback microinverter, within the power range of 200 W, DCM has the advantage over BCM. For simplicity, 1Φ DCM represents only one phase operation and 2Φ DCM represents two phases operation under the interleaved mode. On the one hand, the 2Φ DCM operation shares the current and reduces the current stress between two interleaved phases. This is beneficial to reduce the conduction loss and turn-off loss of the power MOSFETs and diodes, as well as the copper loss of the transformer under heavy load condition. On the other hand, the 1Φ DCM operation shields the additional phase of

4 the micro-inverter, which minimizes the gate driving loss of the power MOSFETs as well as the core loss of the transformer under light load condition. B. Proposed Hybrid Control Method From the analysis above, it is interesting to notice that the advantage of 2Φ DCM operation is current sharing between two phases. The conduction loss and turn-off loss of the power MOSFETs and diodes and the copper loss of the transformer can be reduced when the load current is high. The 1Φ DCM operation reduces the driving loss of the power MOSFETs and the transformer core loss. The conventional DCM control only shuts down one phase when the load reduces to some power level. Actually, during the half line period, either 2Φ DCM or 1Φ DCM control can be applied. It is noticed that the output power pout (t) during a half line period is a pulsating power following a squared sine wave. p (t) = 2P sin (ωt) (1) where Po presents the average value of the output power delivered to the grid. The idea here is to combine the advantages of 2Φ DCM and 1Φ DCM adaptively to the load current during a half line period, which is similar to the phase shedding technology [18]-[19], so that the efficiency can be optimized in wide load rang. Fig.4 shows the operating region of 1Φ DCM and 2Φ DCM during a half line period. In Fig.4, 2Φ DCM is employed when load current is high and 1Φ DCM is employed when the load current under a certain level. In this way, the dominant losses are reduced depending on the load current and higher efficiency can be achieved in wide load range. It should be noted that as Po decreases, the 2Φ DCM region decreases simultaneously. In particular, when Po decreases to a certain level, the hybrid modulation merges into only 1Φ DCM. In additional, it should be noted that 2Φ DCM and 1Φ DCM modulations operate simultaneously during a half line period since the proposed control is based on the instantaneous power delivered to the grid. Fig.4 The output power curve with 1Φ DCM and 2ΦDCM for the interleaved flyback micro-inverter C. Analysis and Design of Reference Signal for the Proposed Control For the proposed control method, the reference signal iref is used to generate the modulated duty cycles and needs to be well designed so that high efficiency and low THD can be achieved. Since the equivalent circuits of the two modules are similar, DCM of a single phase flyback inverter is analyzed firstly. Fig.5 shows the equivalent circuit of the single flyback inverter during a half line period. Fig.5 Equivalent circuit of a single phase flyback inverter During the S1 on time, the primary current ip increases gradually in a linear relationship with the input voltage Vdc and the primary inductance Lp. During the S1 off time, the second current is decreases in a linear relationship with the gird voltage vg (t) and the secondary inductance Ls. The turn-on time Ton and turn-off time Toff in every switching period are T =. (2) T =. (3) () where Ip and Is are the peak value of ip and is in each switching period respectively. Since Ip equals the reference signal iref, the relationships of Ip and Is are I = i (4) I = I. = i. (5) There is an approximation relationship as (6), where the RMS value of the output current iout equals the average value of is in every switching period i =. (6) Considering the above equations, the relationship between iout and iref is i = sin(ωt).. = 2 sin(ωt). (7) where Iout is the peak value of iout; Vo is the peak value of vg (t) and Po1 is the average output power of each phase. For 2Φ DCM operation, Po=2Po1. The above equation can be rewritten as i = sin(ωt). (8)

5 D. Optimal Boundary Condition of 2Φ DCM and 1Φ DCM For the interleaved flyback micro-inverter with the proposed control method, the current reference iref1 and iref2 during a half line period are i = 2 sin(ωt). (t < t, t > t ) sin(ωt). (t < t < t ) (9) i = sin(ωt) (t. < t < t ) (10) Under light load condition, 1Φ DCM operation reduces the driving loss of the power MOSFETs and the transformer core loss. As the power level increases, the conduction losses and turnoff loss of power MOSFETs and diodes as well as the loss of the transformer become the dominant losses. 2Φ DCM operation shares the current between two interleaved phases. The idea is to minimize the dominant losses depending on the load condition. As a result, tc1 and tc2 can be obtained from (11) as shown in Fig.4. sin(ωt ) = sin(ωt ) = = (11) E. Control issues : In the flyback micro inverter with hybrid mode, the current controller should ensure the reference tracking and disturbance rejection performances in both operation regions. Fig5. shows the equivalent circuit of the grid-connected flyback micro- inverter. Using the control input-to-output current transfer function introduced in the transfer function Gid_DCM in DCM can be expressed as follows: G = (13), where Vg,rms is the rms value of the grid voltage. Eqn. (13) is noted that the system gain in DCM is constant and very low at all frequency ranges. Using a small signal modeling, the transfer function Gid BCM in BCM can be represented as G = (14) Where ( ) A = R C B = V + D I R From (14), it is observed that the control input-tooutput current transfer function in BCM has an RHP zero. The RHP zero varies according to the operating points, and its minimum value is at the peak of the grid voltage under maximum output power. Thus, the minimum RHP zero should be considered when the controller for the flyback inverter with hybrid mode is designed. Proposed control strategy : To satisfy the desired control performance and stability in both operation modes, the PR controller can be developed, and its transfer function is expressed as C (s) = k + (15) where kr is the resonant gain. The PR controller in (15) has an infinite gain at the grid frequency. However, the infinite gain would degrade the control performance and even cause the system to become unstable. In the practical implementation, the following form of the PR controller can be adopted as C (s) = k + (16) where ωc is chosen to widen the controller bandwidth and determines the -3 db cutoff frequency of the controller. That is, the magnitude of the compensator becomes kr / 2 at ω-ωc or ω+ωc. In case of the proposed PR controller, the gains kr and ωc are 20 and 16, respectively; In addition, the harmonic compensator is able to alleviate errors for the selective harmonic frequencies, and its transfer function is represented as C (s) =,, (17) where h is the harmonic order, and krh is the resonant gain for each harmonic frequency. The open-loop Bode plots of compensated system by the PR controller with the 3rd to 7th harmonic compensators is shown in Fig.6. The 3rd, 5th, and 7th harmonics are the most prominent harmonics under the grid environment. Like the PR controller, HC provides the high gain at selected harmonic frequency components, which helps eliminating steady-state error and the disturbance by the selected frequency components. The overall proposed control system for the flyback inverter with hybrid mode is shown in Fig.7 it consists of the PR controller with HC and the nominal duty ratio Dn. Ig * is the peak value of the reference grid current (or output current). To classify the section of operation modes without an additional current sensor, the critical duty ratio in can be used; it is noted that the flyback inverter operates in the DCM region when the following condition is satisfied as D (t) D (t) (18) Thus, the hybrid nominal duty ratio Dn in the proposed control strategy is determined as follows: D (t) = D (t) ifd (t) D (t) (19) D (t), ifd (t) D (t) Finally, the proposed hybrid nominal duty ratio can significantly reduce the disturbance effect in

6 both operation modes, and so improve the performance of the feedback controller. (a) (b) Fig.6. Open-loop Bode plots of the compensated system by the proposed controller. (a) In DCM. (b) In BCM. Fig.7. The block diagram of the proposed control system. IV. DESIGN PROCEDURE AND IMPLENMENTIATION A. Design Example Based on the analysis above, the interleaved flyback inverter of 200 W is presented as a design example and verifies the proposed hybrid control method. The specifications are as follows: input voltage (maximum power point): Vdc=50 V; grid voltage: 220 VAC; grid frequency: fgrid=50 Hz; switching frequency: fs=100 khz; transformer turns ratio: n=np/ns=0.5. It should be mentioned that the turns ratio has a close relationship with the voltage and current stress of each component. A small turns ratio leads to a higher primary current stress and a higher secondary voltage stress. On the contrary, a larger turns ratio leads to a higher primary voltage stress and a higher secondary current stress. From (2) and (3), the peak of the primary and secondary current Ip,p and Is,p are I. =. =. (20) I. = (21) where Ton,max is the maximum turn-on time, and dmax is the maximum duty cycle. Combining (5), (20) and (21), the turn-off time Toff is T = = = constant (22) where λ is the ratio of Vdc/Vo. For Vdc=50 V and Vo=311 V, λ is In order to reassure the micro-inverter will always under DCM, it has to be confirmed that the Toff interval is smaller than the time interval between the switching period and the Ton interval. T T T, (23) Combing (20), (22) and (23), the maximum duty cycle dmax is d (1 + ) (24) For λ=0.161 and n=0.5, dmax is less than The average of the primary current during a half line period is I, = i (t)dt (25) Where () i (t)dt = () () dt = T d sin (26) Combining (25) and (26), Ip,avg is I, = sin = = (27) The input power is P = 2V I, = T sv dc 2 2 dmax 2L p (28) For Ppv=200 W, Vdc=50 V and dmax=0.757, the maximum transformer primary inductance Lp_max=35.79 μh. With Lp =0.8Lp_max=28 μh, and the maximum duty cycle dmax is According the specifications of the interleaved flyback micro-inverter, the reference signals of the primary and secondary current are

7 16.90 sin(100πt) t < i = sin(100πt) (, t > < t < ) (29) i = sin(100πt)( < t < ) (30) The waveforms of the reference signals of Phase 1 and Phase 2 for the interleaved flyback micro-inverter with the proposed control method under full load condition are shown in Fig.8 B. Realization of MPPT The PV array under uniform irradiance exhibits a current-voltage characteristic with a unique point, called the maximum power point (MPP), where the array produces maximum output power. Fig.11 (a) shows an example of the PV module characteristics in terms of the PV output current versus the voltage. Fig.11 (b) shows the output power versus the current for different irradiance levels G. As noted in Fig.11, since the I-V characteristic of the PV array, and hence its MPP, changes as a consequence of the variation of the irradiance level, it is necessary to track continuously the MPP in order to maximize the power output from a PV system as far as the PV system efficiency is concerned. Fig.8 Reference signals of Phase 1 and Phase2: full load condition With the same design method, the primary current reference signals of Phase 1 and Phase 2 under half load and quarter load condition can be calculated as illustrated in Fig.9 and Fig.10. Comparing Fig.8 and Fig.9, it is observed that as the power level decreases, the 2Φ DCM region decreases simultaneously. When the power level decreases below 50 W, the hybrid modulation with 2Φ DCM and 1Φ DCM merges into only 1Φ DCM region as shown in Fig.13. (a) Output current versus voltage Fig.9 Reference signals of Phase 1 and Phase2: half load condition Fig.10 Reference signals of Phase 1 and Phase2: quarter load condition (b) Output power versus voltage Fig.11 PV module characteristics for different irradiance levels G C. Design of The Input Capacitance For the single-stage grid-connected microinverter, the MPPT provides the constant output power from the PV panel Ppv, while the power transferred to the grid pout (t) is a pulsating waveform. Generally, the electrolytic capacitor is used to measure the unbalance of the input and output power. When Ppv is surplus to pout (t), the reminded power is stored into the decoupling capacitor. On the contrary, when Ppv is smaller than pout (t), the decoupling capacitor delivers the power to the output. The input and output waveforms are shown in Fig.12.The value of the decoupling capacitor is

8 determined by the energy has to be stored in the capacitor, whose size is C = (31) where ω is the angle frequency of the grid voltage, and ΔV is the maximum peak to peak ripple voltage of the input capacitor. For Ppv=200 W, ω=2πf=100π, Vdc=50 V and ΔV=2 V, the required input capacitance is Cdc=6.37 mf. Four 1.8 mf electrolytic capacitors are paralleled with lower ESR. current stress in both primary and secondary sides than those of the DCM flyback inverter. Fig. 18 represents efficiency comparison for the two flyback inverters according to load conditions; it is obvious that the flyback inverter with hybrid mode has higher efficiency over all load conditions. Its maximum efficiency is measured to be 96.1%. Fig.12 The input and output waveforms V. SIMULATION RESULTS To verify the feasibility and performance of the proposed control strategy, the simulation by a simulator Psim and experiment using the prototype for the flyback micro inverter shown in Fig. 1 were conducted. The nominal PV voltage and rated power were set up to 60V and 200W, respectively. Fig. 14. Simulation results for the grid current ig and its reference ig_ref when the conventional control system is applied. (a) Quarter-load condition. (b) Full-load condition. (a) Fig.13 Block diagram of simulation Fig.15 shows the waveforms for the grid voltage and current when the proposed control strategy is applied. As shown in Fig, regardless of load conditions, the grid current has an almost perfect sinusoidal form and desired power level. The THD on the grid current is measured as 2.4% under fullload condition. Fig. 16 shows the dynamic performance under the load variation. Fig. 17 shows the current stress between the interleaved flyback inverter with hybrid mode and the interleaved flyback inverter operating only in DCM region. To ensure DCM operation for all operating points, the magnetizing inductance of the DCM flyback is set to 11uH. From Fig.16, it is observed that the flyback with hybrid mode has much lower (b) Fig. 15. Simulation results for the grid current ig and its reference ig_ref when the proposed control system is applied. (a) Quarter-load condition. (b) Full-load condition. Fig. 16. Experimental result on the transient response under load variation from full-load to quarter-load.

9 (a) (b) Fig. 17. Comparison for current stress under full-load condition. (a) In a interleaved DCM flyback inverter. (b) In a interleaved flyback inverter with hybrid mode. Fig. 18. Efficiency comparison according to load conditions. VI. CONCLUSION In this paper, the loss distribution and the efficiency of the interleaved flyback micro-inverter under BCM and DCM are investigated analytically under different power levels. It is found that DCM is a better choice than BCM within the power range of 200 W. The 2Φ DCM operation shares the current and reduces the current stress between two interleaved phases. The conduction loss and turn off loss of the power MOSFETs and diodes and the copper loss of the transformer can be reduced at heavy load, and the 1Φ DCM reduces the driving loss of the main MOSFETs and the core loss of the transformer under light load condition. Anew hybrid control strategy combining the 2Φ DCM and 1Φ DCM control during a half line period is proposed. The current control strategy of the flyback micro inverter with hybrid mode for PV ac module has been introduced and verified by the analysis, simulation, and experimental results. In the proposed control strategy, the PR controller with HC provides the high system gain at fundamental and harmonic frequencies in both operation modes without using high proportional gain. The characteristic alleviates the trade-off between the control performance in DCM and stability in BCM when the conventional PI controller is used. In addition, the proposed hybrid nominal duty ratio yielded from the proposed operation mode selection eliminates the disturbance more effectively and reduces the burden of the feedback controller. From the simulation and experiment results, it is verified that the proposed control strategy shows faster reference tracking and better disturbance rejection than those of the conventional strategy REFERENCES [1] 0-scenario.html [2] S. Jiang, D. Cao, Y. Li and F. Z. Peng, Grid-connected boost-half-bridge photovoltaic micro inverter system using repetitive current control and maximum power point tracking, IEEE Trans. on Power Electronics, Vol. 27, No. 11, pp , Nov [3] Z. Liang, R. Guo, J. Li and A. Q. Huang, A high-efficiency PV module-integrated DC/DC converter for PV energy harvest in FREEDM system, IEEE Trans. on Power Electronics, Vol. 26, No. 3, pp , March [4] Prapanavarat, M. Barnes, and N. Jenkins, Investigation of the performance of a photovoltaic AC module, in Proc. IEEE Gener., Trans. Distrib., Vol. 149, No. 4, pp , Jul [5] T. Shimizu and S. Suzuki, Control of a high efficiency PV inverter with power decoupling function, in Proc. IEEE ECCE Asia, 2011, pp [6] N. Kutkut and H. Hu, Photovoltaic microinverter: topologies, control aspects, reliability issues, and applicable standards, in Proc. IEEE Energy Conversion Congress and Exposition (ECCE), 2010, tutorial. [7] T. Shimizu, K. Wada and N. Nakamura, Flyback type single-phase utility interactive inverter with power pulsation decoupling on the DC input for an AC photovoltaic module system, IEEE Trans. on Power Electronics, Vol. 21, No. 5, pp , Sep [8] C. Kyritsis, E.C. Tatakis and N. P. Papanikolaou, Optimum design of the currentsource flyback inverter for decentralized gridconnected photovoltaic systems, IEEE Trans. on Energy Conversion, Vol. 23, No. 1, pp , March [9] C. Nanakos, E. C. Tatakis and N. P. Papanikolaou, A weighted-efficiency-oriented Design Methodology of flyback inverter for AC photovoltaic modules, IEEE Trans. on Power

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