Compact Single-Stage Micro-Inverter with Advanced Control Schemes for Photovoltaic Systems

This paper proposes a grid-connected single-stage micro-inverter with low cost, small size, and high efficiency to drive a 320 W class photovoltaic panel. This micro-inverter has a new and advanced topology that consists of an interleaved boost converter, a full-bridge converter, and a voltage doubler. Variable switching frequency and advanced burst control schemes were devised and implemented. A 320 W prototype micro-inverter was very compact and slim with 60-mm width, 310-mm length, and 30-mm height. In evaluations, the proposed micro-inverter achieved CEC weighted efficiency of 95.55%, MPPT efficiency >95% over the entire load range, and THD 2.65% at the rated power. The proposed micro-inverter is well suited for photovoltaic micro-inverter applications that require low cost, small size, high efficiency, and low noise.


Introduction
The photovoltaic (PV) generation is emerging as a future energy system because of its installation convenience, no-noise, infinite, and eco-friendly characteristics [1][2][3][4].It is classified into the centralized power system and the distributed power system depending on the scale of solar power generation [5].The centralized power system has a simple circuit structure with PV strings as the input energy source, but it has a disadvantage that the power generation is considerably lowered when some panels of the PV string are shaded.On the other hand, in the distributed power system, the optimal power extraction is possible because the maximum power point tracking (MPPT) control can be applied to each PV panel with a micro-inverter connected.So, it can minimize the loss of power generation caused by the shading effect.However, one micro-inverter is required for each PV panel, so implementation of this strategy is expensive.Therefore, many attempts have recently been made to lower the cost of micro-inverters.
In general, considering the cost, micro-inverters have been designed to use circuit architectures with a flyback converter [6][7][8][9][10], which provides galvanic isolation with fewer switches than other designs.Although the flyback converter has the advantage of circuit simplicity and low cost, the design must use a transformer with a high turns ratio to achieve a high voltage-conversion ratio from low dc voltage on a single PV panel.In the transformer, the high turns ratio causes a large leakage inductance which increases the stress on semiconductor switches.Moreover, due to low utilization of the transformer, this topology is most suitable for low-power applications <200 W. Recently, multi-phase interleaved technology has been applied to solar power generation from PV panels that output ≥320 W, but this technology requires large and expensive components.
phase interleaved technology has been applied to solar power generation from PV panels that output ≥320 W, but this technology requires large and expensive components.
This paper proposes a low-cost, slim, single-stage micro-inverter to drive a 320-W-class PV panel.The proposed micro-inverter has an interleaved structure based on the boost half-bridge (BHB) converter [11] with a cascaded voltage doubler.The interleaved BHB has an inversely-coupled inductor for the voltage step-up operation.The coupled inductor can reduce input ripple current and can be reduced in size.The voltage doubler increases the ac output voltage from the interleaved converter.Therefore, the transformer can have a lower turns ratio in the interleaved BHB than in a flyback converter and can be reduced in size.In the proposed micro-inverter, semiconductor switches achieve turn-on zero-voltage-switching (ZVS) and turn-off zero-current-switching (ZCS) by exploiting the resonance between the leakage inductance of the transformer and output capacitors of the voltage doubler, without additional components.
This paper also presents two advanced control algorithms.First, a variable switching frequency control scheme was implemented to reduce total harmonic distortion (THD) by reducing output ripple current.Then an advanced burst control scheme was implemented to improve powerconversion efficiency at light loads.By distributing output current temporally at light loads, input ripple voltage can be reduced.Therefore, the size of decoupling capacitors is reduced and MPPT efficiency is improved compared with the conventional burst control [12][13].Section 2 describes the circuit structure and operating principles of the proposed micro-inverter, Section 3 gives the proposed control schemes, Section 4 shows experimental results using a 320-W prototype microinverter, and Section 5 concludes the paper.The proposed micro-inverter (Figure 1) consists of an interleaved boost converter, a full-bridge converter, and a voltage doubler.The portion that is composed of the interleaved boost and fullbridge converters is based on a boost half-bridge topology.The interleaved boost converter consists of an inversely-coupled inductor LB, four switches S1-S4, and a storage capacitor CS.The full-bridge converter consists of a transformer T1 and the same four switches S1-S4 as the interleaved boost In the proposed interleaved boost converter, two inductors L 1 and L 2 form L B (Figure 2) by using a single magnetic core instead of two separate magnetic cores used in the conventional interleaved boost converter [14].L B has a turns ratio of 1:1; L 1 and L 2 each have self-inductance L. The mutual inductance M between L 1 and L 2 is represented as: where k is the coupling coefficient.The voltage drops of L 1 and L 2 are given, respectively, by

Circuit Structure and Operating Principles of the Proposed Micro-inverter
and Using Equations ( 2) and ( 3) and v m = −Md(i and S 1 , the body diode of S 2 , and L 1 form one boost power stage.S 3 , the body diode of S 4 and L 2 form the other boost power stage.The two boost power stages form an interleaved boost converter and two outputs operate out of phase.When S 1 or S 3 is turned on, voltage v I N is applied to L 1 or L 2 , respectively.When S 1 or S 3 is turned off, voltage v I N − v Cs is applied to L 1 or L 2 , respectively.The energy accumulated during the on-state for each boost power stage is transferred into C S .There are four cases of the voltage v 1 of L 1 and the voltage v 2 of L 2 depending on the states of S 1 and S 3 .Using Equations ( 4) and ( 5), the equivalent inductance for each case is obtained (Table 1).M < 0 in Equation (1), so Table 1 demonstrates that appropriate design of the inversely coupled inductor can reduce the input ripple current of the micro-inverter [15].
ficiency is improved compared with the conventional burst control [12][13].Section 2 describes th rcuit structure and operating principles of the proposed micro-inverter, Section 3 gives th oposed control schemes, Section 4 shows experimental results using a 320-W prototype micr verter, and Section 5 concludes the paper.The proposed micro-inverter (Figure 1) consists of an interleaved boost converter, a full-bridg nverter, and a voltage doubler.The portion that is composed of the interleaved boost and fu idge converters is based on a boost half-bridge topology.The interleaved boost converter consis an inversely-coupled inductor LB, four switches S1-S4, and a storage capacitor CS.The full-bridg nverter consists of a transformer T1 and the same four switches S1-S4 as the interleaved boo nverter.The voltage doubler has four switches S5-S8 and two capacitors C1 and C2.

Symbol
Value Condition The full-bridge converter shares four switches S 1 -S 4 with the interleaved boost converter, and its input power comes from C S .The leakage inductance L lk of T 1 and capacitors C 1 and C 2 in the voltage doubler form an LC resonant circuit.The LC resonant current flows through the primary and secondary sides of T 1 with turns ratio n 1 :n 2 .This current causes the body diode of each switch to conduct before the turn-on gate signal is applied, thus achieving zero-voltage-switching (ZVS) for S 1 -S 4 .
In the voltage doubler, S 5 -S 8 rectify current on the secondary side of T 1 .When grid voltage is positive, both S 5 and S 8 are turned on, and both S 6 and S 7 act as diodes.When grid voltage is negative, both S 6 and S 7 are turned on, and both S 5 and S 8 act as diodes.The energy transferred to the voltage Energies 2019, 12, 1234 doubler through T 1 is stored in C 1 and C 2 .C 1 and C 2 are connected in series, and the output voltage of the micro-inverter is the sum of the voltage v C1 of C 1 and the voltage v C2 of C 2 .
In the proposed micro-inverter, variable-switching-frequency control is used, and the output voltage is a sinusoidal grid voltage.However, for simplicity, the analysis is based on the assumption that the micro-inverter generates a constant output voltage with a fixed switching frequency at a certain point in the analysis.In addition, the electrical losses of all components are ignored, and the following conditions are assumed: 2π L lk (C 1 + C 2 ) > DT s and n 2 L m >> L lk , where L m is the magnetizing inductance and T s is the switching period.The operation cycle S 1 -S 4 is the same regardless of the polarity of the grid voltage, so the analysis considers only positive grid voltage.
The operating waveforms (Figure 3) of the proposed micro-inverter depend on the duty ratio D. First, operational states are analyzed for D ≤ 0.5 (Figures 3a and 4).In the proposed micro-inverter, variable-switching-frequency control is used, and the output voltage is a sinusoidal grid voltage.However, for simplicity, the analysis is based on the assumption that the micro-inverter generates a constant output voltage with a fixed switching frequency at a certain point in the analysis.In addition, the electrical losses of all components are ignored, and the following conditions are assumed: 2  ( +  ) >  and   >>  , where Lm is the magnetizing inductance and Ts is the switching period.The operation cycle S1-S4 is the same regardless of the polarity of the grid voltage, so the analysis considers only positive grid voltage.The operating waveforms (Figures 3) of the proposed micro-inverter depend on the duty ratio D. First, operational states are analyzed for D ≤ 0.5 (Figures 3a, 4).
State 1 (t0-t1): At t = t0, S1 is turned on, vDS1 = 0, and iSW1 < 0. S4 remains in the turn-on state, and both S2 and S3 remain in the turn-off state.For T1, the voltage vLm across Lm is equal to vCs, and the secondary voltage vs proportional to the turns ratio n1:n2 is generated on the secondary side of T1.The magnetizing current iLm is increased and is given by:   Resonance is generated by Llk on the secondary side of T1 and capacitors C1 and C2, and the state equation is given by Using Equations ( 7) and ( 8), the secondary current is of T1 is obtained as where is the resonant impedance and is the resonant angular frequency.
From Equations ( 6) and ( 9), the primary current ip of T1 is obtained as  State 1 (t 0 -t 1 ): At t = t 0 , S 1 is turned on, v DS1 = 0, and i SW1 < 0. S 4 remains in the turn-on state, and both S 2 and S 3 remain in the turn-off state.For T 1 , the voltage v Lm across L m is equal to v Cs , and the secondary voltage v s proportional to the turns ratio n 1 :n 2 is generated on the secondary side of T 1 .The magnetizing current i Lm is increased and is given by: Resonance is generated by L lk on the secondary side of T 1 and capacitors C 1 and C 2 , and the state equation is given by Using Equations ( 7) and ( 8), the secondary current i s of T 1 is obtained as where is the resonant impedance and Energies 2019, 12, 1234 6 of 15 is the resonant angular frequency.
From Equations ( 6) and ( 9), the primary current i p of T 1 is obtained as From Table 1, the currents i L1 and i L2 of the coupled inductor are obtained as State 2 (t 1 -t 2 ): At t = t 1 , S 1 is turned off and S 4 remains in the turn-on state.Both S 2 and S 3 remain in the turn-off state.This interval is a dead time to prevent shoot-through before S 2 is turned on.During this state, the drain-source voltage of S 1 increases from 0 V to v Cs and that of S 2 decreases from v Cs to 0 V by charging and discharging parallel capacitance across each switch, respectively.
State 3 (t 2 -t 3 ): At t = t 2 , S 2 is turned on, v DS2 = 0, and i SW2 < 0. S 4 remains in the turn-on state, and both S 1 and S 3 remain in the turn-off state.For T 1 , the voltage v Lm across L m is 0 V and the voltage v lk across L lk is -v C1 .The amplitude of i Lm remains unchanged during state 3 as: i s begins to decrease because the energy stored in L lk is transferred to C 1 , and is given by From Equations ( 14) and ( 15), i p is obtained as From Table 1, i L1 and i L2 are obtained as State 4 (t 3 -t 4 ): At t = t 3 , S 4 is turned off and S 2 remains in the turn-on state.Both S 1 and S 3 remain in the turn-off state.This time interval is a dead time to prevent shoot-through before S 3 is turned on.During this state, the drain-source voltage of S 4 increases from 0 V to v Cs and that of S 3 decreases from v Cs to 0 V.
The proposed micro-inverter has an interleaved structure, so both the operating principle of the next half cycle for D ≤ 0.5 and the operating principle for D > 0.5 are the same as the above analysis except for the switches used.Thus, further analysis for the others is not given.
The voltage gain G v of the proposed micro-inverter is twice the product of the boost converter voltage gain and the full bridge converter voltage gain:

The Proposed Control Schemes
The main controller (Figure 5) for the proposed micro-inverter takes as analog-to-digital inputs the grid voltage v grid , the grid current i g , the input voltage V IN and the input current I IN .The MPPT controller is based on the perturb and observe (P&O) MPPT algorithm [16].This controller determines the amplitude of the reference grid current I g_ref by using I IN and V IN to maximize solar power generation.In the P&O MPPT algorithm used (Figure 6  The phase-locked loop (PLL) generates the phase information |sin θ * | by using vgrid.In the PLL, virtual voltage vq1 is derived from vgrid for phase detection.
where GPLL(s) is PLL gain and Vgrid is the amplitude of vgrid.
From the inverse Laplace transform of vq1(s), where ωt is the actual phase of the grid.
Using equation (20), the other virtual voltage vq2 is obtained as vgrid and vq2 are transformed into the synchronous reference frame as follows:  The phase-locked loop (PLL) generates the phase information |sin θ * | by using vgrid.In the PLL, virtual voltage vq1 is derived from vgrid for phase detection.
where GPLL(s) is PLL gain and Vgrid is the amplitude of vgrid.
From the inverse Laplace transform of vq1(s), where ωt is the actual phase of the grid.
Using equation (20), the other virtual voltage vq2 is obtained as vgrid and vq2 are transformed into the synchronous reference frame as follows: The phase-locked loop (PLL) generates the phase information |sin θ * | by using v grid .In the PLL, virtual voltage v q1 is derived from v grid for phase detection.
where G PLL (s) is PLL gain and V grid is the amplitude of v grid .
From the inverse Laplace transform of v q1 (s), where ωt is the actual phase of the grid.Using equation (20), the other virtual voltage v q2 is obtained as v grid and v q2 are transformed into the synchronous reference frame as follows: where θ * is a phase output from the PLL.From Equation ( 22), The PLL generates θ * to follow ωt through PI control inside the PLL.The reference current signal i g_ref is the product of I g_ref and |sin θ * |: The proportional-integral (PI) controller determines the duty ratio variation ∆D by using the difference between i g_ref and |i g | as follows: ∆D compensates for the voltage drop L lk , so that i g follows i g_ref .The nominal duty ratio provides stable system dynamics for nonlinear sinusoidal waves which are difficult to control using only ∆D.The total duty ratio where D n is duty ratio generated by the grid voltage and ∆D is a duty ratio variation generated by the grid current.D is given to the pulse-width-modulation (PWM) controller.The PWM controller generates gate signals for switches to track the reference power.Operating modes (Figure 7) depend on the grid current level when grid voltage is positive.When i g is low, the proposed micro-inverter operates in discontinuous conduction mode (DCM) because i g becomes zero before the end of the switching cycle with the period T s .When i g is high, continuous conduction mode (CCM) is applied.
If a fixed switching frequency is used for the operating modes, especially the DCM mode, two problems occur: (1) High grid current ripples at low grid currents increase total harmonic distortion (THD); (2) as the output power decreases, the total DCM operating time can increase over the total CCM operating time, and the power conversion efficiency of the micro-inverter can be reduced by high current stress.To solve these problems, this paper proposes two advanced control schemes: Variable-switching-frequency (VSF) control and the advanced burst (AB) control.
where Dn is duty ratio generated by the grid voltage and ΔD is a duty ratio variation generated by the grid current.D is given to the pulse-width-modulation (PWM) controller.The PWM controller generates gate signals for switches to track the reference power.
Operating modes (Figure 7) depend on the grid current level when grid voltage is positive.When ig is low, the proposed micro-inverter operates in discontinuous conduction mode (DCM) because ig becomes zero before the end of the switching cycle with the period Ts.When ig is high, continuous conduction mode (CCM) is applied.If a fixed switching frequency is used for the operating modes, especially the DCM mode, two problems occur: 1) High grid current ripples at low grid currents increase total harmonic distortion (THD); 2) as the output power decreases, the total DCM operating time can increase over the total CCM operating time, and the power conversion efficiency of the micro-inverter can be reduced by high current stress.To solve these problems, this paper proposes two advanced control schemes: Variable-switching-frequency (VSF) control and the advanced burst (AB) control.

Variable Switching Frequency Control
During T s , i s of T 1 in DCM and CCM modes vary with D (Figure 8).As D decreases, the energy stored in L lk decreases, so time required to demagnetize L lk decreases.Therefore, the micro-inverter is operated in DCM mode.From Equations ( 9) and ( 15), the operating condition for DCM is given by Energies 2019, 12, x FOR PEER REVIEW 9 of 15

Variable Switching Frequency Control
During Ts, is of T1 in DCM and CCM modes vary with D (Figure 8).As D decreases, the energy stored in Llk decreases, so time required to demagnetize Llk decreases.Therefore, the micro-inverter is operated in DCM mode.From Equations ( 9) and ( 15), the operating condition for DCM is given by Existing methods to optimize the DCM mode duration have drawbacks.One method is to increase the value of Llk; a large Llk increases the inductive energy and increases the demagnetizing time, but this solution requires a large transformer with a large number of windings.Another solution is to increase the switching frequency fs; this approach can also increase the power density, but high fs causes high switching loss.Thus, this paper presents VSF control, which minimizes switching loss without increasing the transformer size.VSF control varies fs depending on the magnitude |ig| of the grid current.Fixed-switching-frequency (FSF) control and VSF controls have distinct attributes (Figure 9).FSF control changes only D depending on vgrid (Figure 9a).In contrast, VSF control changes both D and fs Existing methods to optimize the DCM mode duration have drawbacks.One method is to increase the value of L lk ; a large L lk increases the inductive energy and increases the demagnetizing time, but this solution requires a large transformer with a large number of windings.Another solution is to increase the switching frequency f s ; this approach can also increase the power density, but high f s causes high switching loss.Thus, this paper presents VSF control, which minimizes switching loss without increasing the transformer size.VSF control varies f s depending on the magnitude |i g | of the grid current.
Fixed-switching-frequency (FSF) control and VSF controls have distinct attributes (Figure 9).FSF control changes only D depending on v grid (Figure 9a).In contrast, VSF control changes both D and f s depending on v grid (Figure 9b).When v grid is near zero, the switching loss is very small because i g is close to zero.Therefore, when VSF control is used, f s is increased to the maximum switching frequency f max and the time interval between demagnetizings of L lk is reduced (Figure 9b).As v grid increases, f s is decreased to the minimum switching frequency f min to reduce switching losses.f s is given by where V grid is the peak value of v grid . Energies increase the value of Llk; a large Llk increases the inductive energy and increases the demagnetizing time, but this solution requires a large transformer with a large number of windings.Another solution is to increase the switching frequency fs; this approach can also increase the power density, but high fs causes high switching loss.Thus, this paper presents VSF control, which minimizes switching loss without increasing the transformer size.VSF control varies fs depending on the magnitude |ig| of the grid current.Fixed-switching-frequency (FSF) control and VSF controls have distinct attributes (Figure 9).FSF control changes only D depending on vgrid (Figure 9a).In contrast, VSF control changes both D and fs depending on vgrid (Figure 9b).When vgrid is near zero, the switching loss is very small because ig is close to zero.Therefore, when VSF control is used, fs is increased to the maximum switching frequency fmax and the time interval between demagnetizings of Llk is reduced (Figure 9b).As vgrid increases, fs is decreased to the minimum switching frequency fmin to reduce switching losses.fs is given by

Advanced Burst Control
When solar power generation and load are very small, micro-inverters operate only intermittently to supply the desired power to the grid on an average power basis.This intermittent operation is called "burst control".For the burst control, the micro-inverter supplies i g to the grid only during the ON state, and stops running during the OFF state.The burst control improves power-conversion efficiency by reducing the ripple of i g and switching loss when the load is small.
In the conventional burst control scheme, positive and negative grid currents are consecutively supplied to the grid during one ON-state period (Figure 10).Then OFF-state periods follow the ON-state period.During the OFF state, no power is output, so output occurs only during the ON state, and the energy flowing out of C IN is also concentrated.Therefore, the input ripple voltage ∆V IN is increased, the MPPT efficiency is reduced, and additional time is required to charge the input capacitor C IN for the next operation.
where Vgrid is the peak value of vgrid.

Advanced Burst Control
When solar power generation and load are very small, micro-inverters operate only intermittently to supply the desired power to the grid on an average power basis.This intermittent operation is called "burst control".For the burst control, the micro-inverter supplies ig to the grid only during the ON state, and stops running during the OFF state.The burst control improves powerconversion efficiency by reducing the ripple of ig and switching loss when the load is small.
In the conventional burst control scheme, positive and negative grid currents are consecutively supplied to the grid during one ON-state period (Figure 10).Then OFF-state periods follow the ONstate period.During the OFF state, no power is output, so output occurs only during the ON state, and the energy flowing out of CIN is also concentrated.Therefore, the input ripple voltage ΔVIN is increased, the MPPT efficiency is reduced, and additional time is required to charge the input capacitor CIN for the next operation.
To further improve the performance of burst control, this paper proposes AB control, which supplies positive grid current during the first ON-state (Figure 10).The negative grid current is supplied during the ON-state that immediately follows the first ON-state period.Then, OFF-state periods follow the ON-state periods.This scheme has the effect of distributing the output current temporally compared with the conventional burst control scheme.Therefore, in the proposed microinverter with the advanced burst control scheme, the MPPT efficiency can be improved, and the input capacitance CIN can be reduced due to the reduced ΔVIN.

Experimental Results
The proposed grid-connected micro-inverter (Figure 11) was designed to operate at the rated power 320 W, VIN = 25 ~ 52 VDC, IIN.max = 12 ADC, and fs = 60 ~ 90 kHz.The grid voltage was 220 Vrms, the grid frequency was 60 Hz, and grid current supplied by the proposed micro-inverter is 0 ~ 1.45 Arms.The proposed micro-inverter was implemented using the circuit parameters given in Table 2.The microcontroller used was a MN103DF35 (PANASONIC).For the PI controller in the main controller, KP and KI were experimentally optimized and set to 9.  To further improve the performance of burst control, this paper proposes AB control, which supplies positive grid current during the first ON-state (Figure 10).The negative grid current is supplied during the ON-state that immediately follows the first ON-state period.Then, OFF-state periods follow the ON-state periods.This scheme has the effect of distributing the output current temporally compared with the conventional burst control scheme.Therefore, in the proposed micro-inverter with the advanced burst control scheme, the MPPT efficiency can be improved, and the input capacitance C IN can be reduced due to the reduced ∆V IN .

Experimental Results
The proposed grid-connected micro-inverter (Figure 11) was designed to operate at the rated power 320 W, V IN = 25~52 V DC , I IN.max = 12 A DC , and f s = 60~90 kHz.The grid voltage was 220 V rms , the grid frequency was 60 Hz, and grid current supplied by the proposed micro-inverter is 0~1.45A rms .The proposed micro-inverter was implemented using the circuit parameters given in Table 2.The microcontroller used was a MN103DF35 (PANASONIC).For the PI controller in the main controller, K P and K I were experimentally optimized and set to 9.5 and 200, respectively.The sampling frequency for analog signals is 20 kHz, and the resolution of the analog-to-digital converter is 12 bits.The turns ratio of L B is 10:10 and that of T Instead of an actual PV module, the photovoltaic simulator ETS600X14CPVF TerraSAS from AMETEK was used as an input source.The solar cell I-V characteristic curve for the experiment was based on that of the NeON®2 PV module from LG electronics.Gate-source and drain-source voltages were obtained for S1 and S2 at D ≤ 0.5 (Figure 12a) and at D > 0.5 (Figure 12b) at VIN = 34 V and vgrid = 220 Vrms /60 Hz.The drain-source voltage vDS1 of S1 drops to 0 V before the gate signal vS1 is applied, so S1 turns on with ZVS.S2 is complementary to S1 and achieves a ZVS turn-on.The operation of S3 and S4 is out of phase with that of S1 and S2, so S3 and S4 can also achieve the ZVS turn-on.
Waveforms (Figure 13) were obtained for vgrid and ig at VIN = 34 V and vgrid = 220Vrms / 60 Hz for output power Po = 320 W and 64 W. To maximize efficiency, the proposed micro-inverter operates in normal mode at Po ≥ 110 W and in AB control mode at Po < 110 W. The boundary of the output power  Instead of an actual PV module, the photovoltaic simulator ETS600X14CPVF TerraSAS from AMETEK was used as an input source.The solar cell I-V characteristic curve for the experiment was based on that of the NeON®2 PV module from LG electronics.
Gate-source and drain-source voltages were obtained for S 1 and S 2 at D ≤ 0.5 (Figure 12a) and at D > 0.5 (Figure 12b) at V IN = 34 V and v grid = 220 V rms /60 Hz.The drain-source voltage v DS1 of S 1 drops to 0 V before the gate signal v S1 is applied, so S 1 turns on with ZVS. S 2 is complementary to S 1 and achieves a ZVS turn-on.The operation of S 3 and S 4 is out of phase with that of S 1 and S 2 , so S 3 and S 4 can also achieve the ZVS turn-on.Waveforms were obtained for the fixed-frequency (Figure 14a) and the variable-switchingfrequency (Figure 14b) controls.Gate signals of S1 and S3, ig and vgrid were measured at VIN = 34 V, vgrid = 220 Vrms / 60 Hz, and output power Po = 320 W. When fixed-switching frequency control was used, ig was distorted near zero-crossing, and THD was increased to 5.79%.In contrast, when variable switching frequency control was used, the distortion of ig was improved near zero-crossing, and THD Waveforms (Figure 13) were obtained for v grid and i g at V IN = 34 V and v grid = 220V rms / 60 Hz for output power P o = 320 W and 64 W. To maximize efficiency, the proposed micro-inverter operates in normal mode at P o ≥ 110 W and in AB control mode at P o < 110 W. The boundary of the output power at which the proposed micro-inverter switches from the normal mode to AB control mode and vice versa is selected to be in a range where the peak value of i g does not exceed the rated grid current.Waveforms were obtained for the fixed-frequency (Figure 14a) and the variable-switching- Waveforms were obtained for the fixed-frequency (Figure 14a) and the variable-switchingfrequency (Figure 14b) controls.Gate signals of S 1 and S 3 , i g and v grid were measured at V IN = 34 V, v grid = 220 V rms / 60 Hz, and output power P o = 320 W. When fixed-switching frequency control was used, i g was distorted near zero-crossing, and THD was increased to 5.79%.In contrast, when variable switching frequency control was used, the distortion of i g was improved near zero-crossing, and THD was reduced to 2.65%, which is below the requirement for distributed power.The switching frequency f s decreased as i g increased, so switching loss was also reduced.
∆V IN is higher when conventional burst control is used (Figure 15a) than when AB control is used (Figure 15b), because AB control reduces the energy supplied by C IN during one ON-state period.At V IN = 34 V, v grid = 220 V rms / 60 Hz, and P o = 32 W, ∆V IN was 4.2 V when conventional burst control was used, but 2.4 V when AB control was used.Waveforms were obtained for the fixed-frequency (Figure 14a) and the variable-switchingfrequency (Figure 14b) controls.Gate signals of S1 and S3, ig and vgrid were measured at VIN = 34 V, vgrid = 220 Vrms / 60 Hz, and output power Po = 320 W. When fixed-switching frequency control was used, ig was distorted near zero-crossing, and THD was increased to 5.79%.In contrast, when variable switching frequency control was used, the distortion of ig was improved near zero-crossing, and THD was reduced to 2.65%, which is below the requirement for distributed power.The switching frequency fs decreased as ig increased, so switching loss was also reduced.ΔVIN is higher when conventional burst control is used (Figure 15a) than when AB control is used (Figure 15b), because AB control reduces the energy supplied by CIN during one ON-state period.At VIN = 34 V, vgrid = 220 Vrms / 60 Hz, and Po = 32 W, ΔVIN was 4.2 V when conventional burst control was used, but 2.4 V when AB control was used.The MPPT efficiency of the proposed micro-inverter was measured (Figure 16) in the range of irradiance from 50 W/m 2 (Po = 16 W)-1000 W/m 2 (Po = 320 W).In the proposed control scheme, for Po < 110 W (burst mode), the MPPT efficiency was kept >95% because ΔVIN and ΔIg_ref are reduced.However, in the conventional control scheme, the MPPT efficiency was reduced to ~88% because fluctuation of Ig_ref increased.During burst mode, the maximum MPPT efficiency was >99% for the proposed control scheme but <97.5% for the conventional control scheme.In a micro-inverter, one of the most important factors is the power conversion efficiency ɳe for 50 ~ 75% load under actual solar irradiation.Therefore, the California Energy Commission (CEC) weighted efficiency to represent this fact has been widely used to measure the performance of microinverters.The power conversion efficiency ɳe (Figure 17) was measured for the proposed microinverter; the result indicate that the CEC weighted efficiency [17][18] is 95.55%, in which ɳe(10%) = 91.71%,ɳe(20%) = 94.42%,ɳe(30%) = 95.28%,ɳe(50%) = 96.06%,ɳe(75%) = 95.8%, and ɳe(100%) = 95.72%.The MPPT efficiency of the proposed micro-inverter was measured (Figure 16) in the range of irradiance from 50 W/m 2 (P o = 16 W)-1000 W/m 2 (P o = 320 W).In the proposed control scheme, for P o < 110 W (burst mode), the MPPT efficiency was kept >95% because ∆V IN and ∆I g_ref are reduced.However, in the conventional control scheme, the MPPT efficiency was reduced to ~88% because fluctuation of I g_ref increased.During burst mode, the maximum MPPT efficiency was >99% for the proposed control scheme but <97.5% for the conventional control scheme.was reduced to 2.65%, which is below the requirement for distributed power.The switching frequency fs decreased as ig increased, so switching loss was also reduced.ΔVIN is higher when conventional burst control is used (Figure 15a) than when AB control is used (Figure 15b), because AB control reduces the energy supplied by CIN during one ON-state period.At VIN = 34 V, vgrid = 220 Vrms / 60 Hz, and Po = 32 W, ΔVIN was 4.2 V when conventional burst control was used, but 2.4 V when AB control was used.The MPPT efficiency of the proposed micro-inverter was measured (Figure 16) in the range of irradiance from 50 W/m 2 (Po = 16 W)-1000 W/m 2 (Po = 320 W).In the proposed control scheme, for Po < 110 W (burst mode), the MPPT efficiency was kept >95% because ΔVIN and ΔIg_ref are reduced.However, in the conventional control scheme, the MPPT efficiency was reduced to ~88% because fluctuation of Ig_ref increased.During burst mode, the maximum MPPT efficiency was >99% for the proposed control scheme but <97.5% for the conventional control scheme.In a micro-inverter, one of the most important factors is the power conversion efficiency ɳe for 50 ~ 75% load under actual solar irradiation.Therefore, the California Energy Commission (CEC) weighted efficiency to represent this fact has been widely used to measure the performance of microinverters.The power conversion efficiency ɳe (Figure 17) was measured for the proposed microinverter; the result indicate that the CEC weighted efficiency [17][18] is 95.55%, in which ɳe(10%) = In a micro-inverter, one of the most important factors is the power conversion efficiency ï e for 50~75% load under actual solar irradiation.Therefore, the California Energy Commission (CEC) weighted efficiency to represent this fact has been widely used to measure the performance of micro-inverters.The power conversion efficiency ï e (Figure 17) was measured for the proposed micro-inverter; the result indicate that the CEC weighted efficiency [17,18] is 95.55%, in which ï e (10%) = 91.71%,ï e (20%) = 94.42%,ï e (30%) = 95.28%,ï e (50%) = 96.06%,ï e (75%) = 95.8%, and ï e (100%) = 95.72%.The maximum ï e is 96.06% for P o = 160 W.

Conclusion
A compact single-stage micro-inverter with advanced control schemes for PV systems is described.The proposed micro-inverter achieved a high voltage-conversion ratio and high efficiency by using a new topology that consists of an interleaved boost converter, a full-bridge converter, and a voltage doubler.The leakage inductance of the transformer and the capacitors of the voltage doubler ensure ZVS condition without any additional components.A variable-switching-frequency control scheme is applied to the micro-inverter to decrease THD by reducing the grid ripple current.An advanced burst-control scheme increases MPPT efficiency with smaller input ripple voltage than the conventional burst control causes.A fabricated 320-W prototype micro-inverter was very compact and slim with 60-mm width, 310-mm length, and 30-mm height.It achieved CEC weighted efficiency of 95.55%, MPPT efficiency > 95% over the entire load rage, and THD 2.65% at VIN = 34 V, vgrid = 220 Vrms / 60 Hz, and Po = 320 W.These results show that the proposed micro-inverter is well suited for PV micro-inverter applications that require low cost, small and slim size, high efficiency, and low noise.

Conclusions
A compact single-stage micro-inverter with advanced control schemes for PV systems is described.The proposed micro-inverter achieved a high voltage-conversion ratio and high efficiency by using a new topology that consists of an interleaved boost converter, a full-bridge converter, and a voltage doubler.The leakage inductance of the transformer and the capacitors of the voltage doubler ensure ZVS condition without any additional components.A variable-switching-frequency control scheme is applied to the micro-inverter to decrease THD by reducing the grid ripple current.An advanced burst-control scheme increases MPPT efficiency with smaller input ripple voltage than the conventional burst control causes.A fabricated 320-W prototype micro-inverter was very compact and slim with 60-mm width, 310-mm length, and 30-mm height.It achieved CEC weighted efficiency of 95.55%, MPPT efficiency > 95% over the entire load rage, and THD 2.65% at V IN = 34 V, v grid = 220 V rms /60 Hz, and P o = 320 W.These results show that the proposed micro-inverter is well suited for PV micro-inverter applications that require low cost, small and slim size, high efficiency, and low noise.

Figure 1 .
Figure 1.The circuit structure of the proposed micro-inverter.

Figure 2 .
Figure 2. The equivalent circuit of the inversely coupled inductor LB.

Figure 1 .
Figure 1.The circuit structure of the proposed micro-inverter.

Figure 1 .
Figure 1.The circuit structure of the proposed micro-inverter.

Figure 2 .
Figure 2. The equivalent circuit of the inversely coupled inductor LB.

Figure 2 .
Figure 2. The equivalent circuit of the inversely coupled inductor L B .

Energies 2019 ,
12,  x FOR PEER REVIEW 4 of 15 doubler through T1 is stored in C1 and C2.C1 and C2 are connected in series, and the output voltage of the micro-inverter is the sum of the voltage vC1 of C1 and the voltage vC2 of C2.

15 Figure 5 .
Figure 5. Block diagram of the main controller for the proposed micro-inverter.

Figure 5 . 15 Figure 5 .
Figure 5. Block diagram of the main controller for the proposed micro-inverter.

Figure 7 .
Figure 7. Operating modes depending on the grid current level during the positive grid voltage.

Figure 7 .
Figure 7. Operating modes depending on the grid current level during the positive grid voltage.

Figure 8 .
Figure 8. Secondary current is of the transformer T1 depending on the operating mode.

Figure 8 .
Figure 8. Secondary current i s of the transformer T 1 depending on the operating mode.

Figure 10 .
Figure 10.Conventional and advanced burst control schemes.
5 and 200, respectively.The sampling frequency for analog signals is 20 kHz, and the resolution of the analog-to-digital converter is 12 bits.The turns ratio of LB is 10:10 and that of T1 is 6:19.The resonant frequency fr = 35.5 kHz from Llk = 100 µH and C1 = C2 = 100 nF.The MOSFET package of S1 -S4 is PG-TDSON-8 and that of S5-S8 is D 2 PAK.Capacitors Cs, C1 and C2 are MPP-film type.The fabricated micro-inverter was compact and slim with 60-mm width, 310-mm length, and 30-mm height.

10 .
Conventional and advanced burst control schemes.
1 is 6:19.The resonant frequency f r = 35.5 kHz from L lk = 100 µH and C 1 = C 2 = 100 nF.The MOSFET package of S 1 -S 4 is PG-TDSON-8 and that of S 5 -S 8 is D 2 PAK.Capacitors C s , C 1 and C 2 are MPP-film type.The fabricated micro-inverter was compact and slim with 60-mm width, 310-mm length, and 30-mm height.Energies 2019, 12, x FOR PEER REVIEW 11 of 15

Figure 11 .
Figure 11.Photograph of the proposed micro-inverter.

Figure 11 .
Figure 11.Photograph of the proposed micro-inverter.

Figure 14 .
Figure 14.Gate signals of S1 and S3, grid voltage and grid current in (a) the fixed and (b) the variable switching frequency controls.

Figure 12 .
Figure 12.Gate-source and drain-source voltages of S 1 and S 3 for (a) D ≤ 0.5 and (b) D > 0.5.

Figure 14 .
Figure 14.Gate signals of S1 and S3, grid voltage and grid current in (a) the fixed and (b) the variable switching frequency controls.

Figure 14 .
Figure 14.Gate signals of S1 and S3, grid voltage and grid current in (a) the fixed and (b) the variable switching frequency controls.

Figure 14 .
Figure 14.Gate signals of S 1 and S 3 , grid voltage and grid current in (a) the fixed and (b) the variable switching frequency controls.

Figure 15 .
Figure 15.Input ripple voltage in (a) the conventional and (b) the advanced burst controls.

Figure 15 .
Figure 15.Input ripple voltage in (a) the conventional and (b) the advanced burst controls.

Figure 15 .
Figure 15.Input ripple voltage in (a) the conventional and (b) the advanced burst controls.

Figure 17 .
Figure 17.Power conversion efficiency ï e measured at V IN = 34 V and v grid = 220 V rms /60 Hz.

Author
Contributions: Y.-G.C. conceived the main idea for the proposed micro-inverter and performed overall analysis and experiment with H.-S.L., B.K. led the project and gave technical advice.S.-C.L. contributed to determining circuit parameters and fabricating a prototype.S.-J.Y. contributed to analyzing the experimental results and writing the manuscript with Y.-G.C.

Table 1 .
Equivalent inductances in the interleaved boost converter.

Table 2 .
Hardware specifications and circuit parameters.

Table 2 .
Hardware specifications and circuit parameters.