Isolated Single-phase AC Grid Connected Converter
With small Inductors and Capacitors for
Micro-inverters
Hiroki Watanabe

Jun-ichi Itoh

Department of Electrical engineering
Nagaoka University of Technology
Niigata, Japanhwatanabe@stn.nagaokaut.ac.jp

Department of Electrical engineering
Nagaoka University of Technology
Niigata, Japan
Itoh@vos.nagaokaut.ac.jp

Abstract— In this paper, a high power density single-phase
inverter for photovoltaic system is presented. The proposed
converter consists of a resonance-type isolated DC/DC converter,a power decoupling circuit and a current source inverter (CSI). In
particular, the volume reduction of capacitors and inductors isfocused. Consequently, a leakage inductor of a center-tapped
transformer is used as a DC inductor instead of a large inductor.
In addition, the reduction of the input voltage ripple into the DCside without a large smoothing inductor or an electrolytic
capacitor is achieved. Finally, the proposed converter also achievesa zero current switching (ZCS) for all switching devices. As asimulation result, the input voltage ripple due to the single-phasepower fluctuation is under than 5%, and the total harmonic
distortion (THD) of the inverter output current is less than 5%. In
addition, the design of the resonance component is discussed. It isobserved from the simulation and the experimental result, that thehigh quality factor Q should be designed in order to achieve thestability of the resonance current.

On the other hand, the micro-inverter with the highfrequency transformer such as a fly-back and a resonance-type
DC/DC converter has been studying. In particular, resonancetype DC/DC converter achieves a ZCS or Zero voltage
Switching (ZVS) utilizing the resonance. However, theconverter efficiency decreases in comparison with the nonisolated type converter because of the transformer loss.

Keywords—Photovoltaic; grid connected inverter; active power
decoupling; flying capacitor DC-DC converter; single-phase power
ripple.

On the other hand, the active power decoupling method can
reduce the capacitance for the instantaneous power fluctuationcompensation, and a small film or a ceramic capacitor can beused instead of the large electrolytic capacitor. In addition, theelimination of the inductor is important for the high power
density design. In particular, the high frequency operation can
reduce the inductance greatly. In this case, the reduction of theswitching losses is the key technology to achieve both the highefficiency and high power density by the active power
decoupling. However, many active power decoupling approachdecreases the converter efficiency due to the additional
components or the switching losses with high the frequency
operation.

I.

INTRODUCTION

Recently, Photovoltaic (PV) system has been researchingactively as a sustainable power solution. In order to achieve theflexibility, high system efficiency, and low manufacturing cost,utilization of the micro-inverters may become a trend for future
PV system instead of using large capacity inverters [1]-[7]. In
particular, the micro-inverter requires the high reliability
because many converter units are adopted to the PV system.
In order to satisfy these requirements, many converter
topologies have been studied [8]-[10]. In general, the power
converter system (PCS) needs the isolation between the PV sideand the single-phase AC grid side because the leakage current
occurs on the power line and the earth ground. Thus, a nonisolated PCS often requires a bulky isolation transformer withcommercial frequency to AC grid side. The micro-inverter
system needs many converter units. Thus the commercial
frequency isolation transformer increase the system volume.

In order to eliminate the large electrolytic capacitor, an
active power decoupling methods have been studied [11]-[17].
In the DC to single-phase AC grid connection system, the large
electrolytic capacitor is required because the instantaneous
power fluctuation at the twice grid frequency occurs due to thesingle-phase AC grid, and it decays the performance of the
maximum power point tracking (MPPT). Besides, theelectrolytic capacitor limits the life-time of the converter due tothe Arrhenius law.

This paper presents an active power decoupling circuit whichis integrated to the CSI and the resonance type isolated DC/DC
converter. The proposed converter compensates theinstantaneous power fluctuation without large electrolytic
capacitors. In addition, ZCS achieves at the all switching devices.
Moreover, the large inductor is not required because the leakage
inductance of the transformer is used as a DC inductor.

This paper is organized as follows: first, the configuration of
the proposed circuit is shown. Next, the principle of the power
decoupling control is described. In addition, the design methodof the isolated DC/DC converter and its validity are explainedwith the simulation and experimental results. Finally, thefundamental operation and each evaluation are confirmed.
II.

CIRCUIT TOPOLOGY

Fig. 1 shows the proposed converter which consists of aresonance-type isolated DC/DC converter, an active power
decoupling circuit, and a CSI. The proposed converter does notneed a large capacitor and inductor because the active power
decoupling can be employed with a small buffer capacitor Cbuf,
and the proposed converter operates at the high switchingfrequency more than one-hundred kHz.
Firstly, the resonance-type isolated DC/DC converter
achieves the ZCS operation using resonance with arm capacitors
C1, C2 and leakage inductance of the transformer Ls. Note that,the switching frequency is set at the resonance frequency, andthe primary side MOSFET S1 and S2 operates with 50% of
switching duty. The resonance frequency is designed to be highin order to reduce the volume of the transformer.
The active power decoupling circuit compensates the powerfluctuation with the small capacitor Cbuf and rectifies the highfrequency resonance current. After that, the high frequency
rectified current flows to the single-phase AC grid or Cbuf. In
order to reduce the switching loss of the active power decoupling
circuit and the CSI, the delta-sigma-based pulse density
modulation (Δ−Σ_PDM) is applied instead of the pulse widthmodulation (PWM). Therefore, ZCS is achieved on the zerocurrent point of the high frequency rectified current.

Fig. 1. Proposed DC to single-phase AC grid connected converter which
is not required large energy buffer. The proposed converter achieves ZCS
on each MOSFETs.

V I
pout = acp acp (1 − cos2ωt )2Fig. 2 Compensation principle of the single-phase power pulsation.
Small buffer capacitor Cbuf eliminates the second-order harmonics on Pin.

As shown in Fig. 1, the proposed converter requires many
switching devices. The main contribution in this paper is theelimination of the large passive components in the circuit
topology, e.g. the large inductor and costly. On the other hand,the cost of the switching devices may become cheap when the
micro-inverter is massively adapted to the PV system.
III.

CONTROL METHOD

A. Principle of single-phase power fluctuation
Fig. 2 shows the principle of the active power decoupling.
When both the output voltage and current waveforms are
sinusoidal, the instantaneous output power pout is expressed as

pout =

Vacp I acp
2(1 − cos 2ωt )(1)where, Vacp is the peak voltage, Iacp is the peak current, and ω isthe angular frequency of the output voltage. As shown in (1), thepower ripple that fluctuates at twice frequency of the AC gridoccurs at DC link.
In order to absorb the power ripple, the instantaneous power
pbuf, should be controlled as in (2)Fig.3 Operation mode of active buffer circuit and CSI. The buffer capacitor ischarged and discharged by mode 2 and mode 3. Each mode is switched at thezero current point of the high frequency pulse current.

2

VCmin −pinωCab{sin(2ωt ) − 1}

Fig. 4 Control block diagram of active power decoupling circuit and CSI.
In order to achieve ZCS, the delta-sigma-based pulse density modulation is applied.

1
pbuf = Vacp I acp cos 2ωt2(2)

where, the polarity of pbuf, is defined as positive when the flying
capacitor Cfc discharges. Note that the active power of the flying
capacitor Cfc is zero. Due to the power decoupling, the input
power is matched to the output power. Thus, the relationshipbetween the input and output power is expressed as1
pin = Vacp I acp = VIN I IN
2

(3)

B. Operation modes of active power decoupling circuit
Fig. 3 shows the operation mode of the active power
decoupling circuit and the CSI when the grid voltage is the
positive. Note that, the current pathway from the single-phasegrid to the small capacitor Cbuf does not occur because thecapacitor voltage is always higher than the peak grid voltage.
The active power decoupling circuit and the CSI are controlled
in four modes defined by the switching pattern in Fig.4. In
mode1, the input power Pin is directly supplied to the singlephase grid. In this control, the buffer power pbuf is controlled
only by mode 2 and mode 3. In mode 2, the small capacitor Cbuf
is charged. In contrast, Cbuf is discharged to the single-phase gridin mode 3. As a result, the small capacitor voltage is fluctuatedat the twice frequency of the single-phase grid. Finally, mode 4
is the freewheeling mode.
In these modes, the active power decoupling circuit isswitched in synchronization with the operation arm dependently
on the resonance current polarity. Consequently, the CSI
operates with the single-phase grid voltage according to thepolarity of the resonance current.

d tempo
d mode2 = 0− d tempo
d mode3 =  0, dc ≥ 0, dc ≤ 0, dc ≤ 0(5), dc ≥ 0

where, Vdc* is the reference value of the input voltage of theactive power decoupling circuit. dc is the duty reference for the
charge and discharge of the buffer capacitor C3. On the other
hand, the buffer capacitor current ic is expressed asic =Vacp I acp
2vc

cos(2ωt )(6)

where, vc is the instantaneous voltage of the buffer capacitor Cbuf.
In addition, ic is decided by the dmode2 ，dmode3 ，and Idc. The
relationship between the duty references and ic is expressed as

ic = (−d mode2 + d mode3) I dc

(7)

According to (6) and (7)，dc is expressed asdc =Vacp I acp
2vc I dccos(2ωt ) =*Vdccos(2ωt )vc(8)where, Vdc* has to be satisfied as in the following condition
*

Vdc ≤

Vacp
2

(9)

This is because the all duty commands should be positive.

C. Control block diagram of proposed circuit
Fig. 4 shows the control block diagram. The duty reference
dmode1, dmode2 and dmode3 are expressed as*

d mode1 = 2

VINsin(ωt ) − d mode3
VINp

(4)

In this control, the buffer capacitor voltage control (AVR)
is operated to compensate the error between the duty references
and the actual voltage. Note that the phase reference is
synchronized to the single-phase AC grid voltage by Phase
Looked Loop (PLL).

D. Modulation method of proposed converter
Fig. 5 shows the modulation block diagram of the Δ−Σ_PDM.
The duty command values dmode1 to dmode3 are converted to theselector signal Sel_mode1 to Sel_mode3 for each operation mode.
First, the error between each duty command and the selector
signal are calculated, and integrated. Next, the quantize outputs
Sel_mode1 to Sel_mode3 corresponding to the integral error. Note
that, quantizes are operated with the quantizing clock (CLK_Q),
and CLK_Q is synchronized with the zero current point of thepulse current. CLK_Q is obtained by the gate signals of the
primary MOSFET because when the transformer power factor
is unity, the zero current point varies corresponding to theprimary transformer current zero cross point. Appling
Δ−Σ_PDM, the active power decoupling circuit and the CSI
achieve the ZCS operation because each MOSFET is switchedat the zero current point of the secondary-side input current.
The secondary input current is supplied from the isolated
resonance DC/DC converter to the active power decoupling
circuit and the CSI. Note that ZCS is achieved based on thiscurrent. Thus, the design of the resonance parameter is importantfor proposed operation.
IV.







Fig. 5 Modulation block diagram of delta-sigma based pulse density
modulation.

DESIGN METHOD OF ISOLATED RESONANCE DC/DC
CONVERTER

A. Fundamental design
Fig. 6 (a) shows the equivalent series resonance model of theisolated DC/DC converter. In this model, the smoothing
capacitor is connected on the rectifier output part in order toeliminate the switching frequency component. In this case, thearm capacitor C1, C2 and the leakage inductance of thetransformer Ls are utilized for the series resonance, and theisolated DC/DC converter achieves the ZCS operation.
Generally, the transformer voltage results in the square
waveforms, and the transformer peak voltage is always the halfof the PV input voltage Vin.
Fig. 6 (b) shows the equivalent model for the proposed
converter. The proposed converter does not adopted theswitching filter between the isolated DC/DC converter and theactive power decoupling circuit because the high frequency
resonance current is utilized for the ZCS operation with theactive power decoupling circuit and the CSI. However, when thesmoothing capacitor is not adopted, the operation of thesecondary converter interferes to the resonance condition. As aresult, the transformer peak voltage fluctuates depending on theoperation mode as shown in Fig.3. Due to this reason, theconventional resonance parameter design cannot be applied forthe proposed converter. In this chapter, a design criterion of theresonance parameters is considered.
Firstly, the resonance frequency fres is expressed as

f res =1
2π (C1 + C 2 ) Ls

(10)

where, the resonance frequency is designed as the highfrequency more than the one-hundred kHz in order to reduce(a)Ideal model for series resonance.

(b) Series resonance model of proposed circuit.
Fig. 6 Equivalent model of series resonance for isolated DC/DC converter.

the volume of the transformer. When the switching frequency
and the resonance frequency becomes the same, the resonancecurrent ires becomes sinusoidal. The peak resonance current Iresis expressed as

4 Vi _ half
π Rs

(11)

where, Vi_half is the primary-sides peak voltage of thetransformer, Rs is the equivalent AC resistance. In this case, Rs
is expressed as2Rs =8  N 1  Vin
π 2  N 2  I in

(12)

Finally, the resonance peak current Ires is derived from (10) and(11)

I res = πI in

Resonance current [Apeak]

I res =

Fig. 7 Characteristics of series resonance current. When the equivalent AC
resistance is same, the resonance current peak become maximum at theresonance frequency.

(13)

B. Determination of LC resonance parameters
When the resonance parameters C1, C2 and Ls are selectedbased on the resonance frequency, many options exists. One of
the criterion is the quality factor Q, and it influences to theresonance frequency characteristics.
The quality factor Q of the series resonance is expressed as

Q=

1
Rs

Ls
C1 + C 2(14)

Fig. 7 shows the resonance frequency characteristics when the
Q value is changed. As shown in Fig.7, the resonance peakcurrent at the resonance frequency is the same with both the low
Q and high Q values.
On the other hand, the resonance voltage is proportional to
the Q value. The resonance peak inductor voltage VLpeak isexpressed as
V Lpeak = QR s I res

Fig. 8 Simulation result of resonance current. The error between thedesign and the simulation value is less than 1%.

(15)

When the resonance parameters is designed at the high Q value,
the resonance voltage on each resonance condition becomeslarge. Thus, each component is required the high rated voltage.
When the series resonance is designed to focus on the highefficiency, the Q value should be low. Because in the low Q
design, the leakage inductance and the resonance peak voltage
can be small from (14) and (15). However, when the Q value isdesign to low, the resonance current peak oscillates due to the
disturbance. The damping coefficient ξ is expressed as
1
ξ =
2Q

(16)

When ξ is high, the resonance current fluctuates unstably, and it
is difficult to sustain the continuity of the series resonance.
Especially, the proposed circuit does not use the switching filter
between the isolated resonance DC/DC converter and thesecondary-side converter. Thus, secondary-side converter
operation interferes the resonance condition as the disturbance.
As a result, the resonance current decays.

Fig. 9 Comparison between resonance current and design value when
output power and input current is changed.

In order to consider the resonance condition on the proposed
converter, two conditions are simulated in next chapter. One isthe low Q value condition, and it is confirmed that the error
between the simulation and the design value becomes large. On
the other hand, in the high Q condition, the simulation value
agrees with the design value.

V.

EVALUATION OF RESONANCE PARAMETER DESIGN

A. Simulation results
Fig. 8 shows the simulation result of the proposed resonancedesign. In this simulation, the Q value is designed to be highvalue, and the resonance frequency is set at 200 kHz. As shownin Fig.8, the error between the design value and the simulation
value is less than 1%, and the resonance current becomes asinusoidal waveforms.
Fig. 9 shows the relationship between the output power andthe resonance peak current. In this result, the input current
condition is changed from 4 A to 6 A. According to Fig. 9, all
the simulation results agree with the design values at thecondition of the high Q value. However, when the Q value islow, the error between the design value and the simulation result
becomes large.

(a)

Lres : 20μH，C : 30nF，Q : 11.

Fig. 10 shows the simulation result with different Q values.
In the Fig. 10 (a), the resonance parameters are designed at the
low Q condition. In addition, the resonance peak current isdesigned to be 15.7A. According to Fig. 10 (a), the maximum
error between the simulation value and the design value is 52%
at the condition of the low Q value.
On the other hand, with the condition of the high Q value in
Fig.10 (b), the error is reduced by 99% in comparison with Fig.
10(a). It is because the transformer peak voltage is fluctuated in
the proposed converter.
The reason why the high error between the simulation value
and the design value occurs at the low Q value is explained asfollowing. The proposed converter does not adopt the switchingfilter on the DC bus, and the resonance current is utilized toachieve ZCS for the active power decoupling circuit and the CSI.
Thus, the secondary-side peak voltage of the transformer
fluctuates. For example, in mode 2, the secondary-side
resonance current flows in the small capacitor Cbuf, and thesecondary-side voltage of the transformer is clamped to thesmall capacitor voltage Vcbuf. On the other hand, in the mode1,
the resonance current is supplied to the single-phase grid. As aresult, the secondary transformer voltage is clamped to the gridvoltage Vac. When the Q value is low, the resonance peak current
is fluctuated severely. This is because the series resonance is
excited by the transformer voltage. However, the same
resonance peak current at the all switching mode is preferable.
In order to suppress the resonance peak current fluctuation, theQ value should be high. This leads to the low damping
coefficient ξ which can sustain the series resonance. Following
these results, when the resonance current is required to agreewith the design value, the Q value of the series resonance has tobecome high.
B. Experimental result of the resonance current design
In order to validity of the proposed design method, two
300W prototype circuits are tested. Table. 1 shows theexperimental parameters. In this experiment, two conditions forthe type isolated resonance DC/DC converter are evaluated. The
only difference between the two converters is the resonanceparameter. Therefore, the same switching device, transformer
cores, windings are selected. Note that, the winding structure isdifferent in order to adjust the leakage inductance. When the Q(b) Lres : 200μH，C : 3nF，Q : 109.
Fig. 10 Resonance current when Q value is changed. When the conditionof the low Q value is employed, the error between the design value andthe simulation value becomes large.
Table.1 Experimental parameters

Fig. 11 Experimental result with ZCS of isolated resonance DC/DC
converter.

value is to be high, the leakage inductance is large. In addition,
the resonance frequency is designed to 150 kHz.
Fig. 11 shows the primary MOSFET switching waveforms.
According to fig.11, the drain-source voltage of S1 is switchedat the zero current point, e.g. the achievement of ZCS. Note that,
ZCS is achieved in both the high Q condition.
Fig. 12 shows the comparison with the resonance peakcurrent and the design value. Note that, the design value iscalculated by (13). As shown in fig.13, the maximum error is
4.5% when the input current is 3.5 A. Furthermore, theresonance current peak is increases proportionally to the input
current. Note that, when ZCS is achieved, the reduction of the
conduction loss of the each MOSFET is important for theachievement of the high efficiency. In this application, theprimary side current of the transformer is large due to the low
voltage condition. Thus, the full bridge type isolated DC/DC
converter is better at the low voltage condition.
Fig. 13 shows the efficiency characteristics in both the highQ condition and the low Q condition. The maximum efficiency
with the low Q value condition is 96.5%. On the other hand, themaximum efficiency with the high Q value is reduced by 2.9%.
This is because the transformer loss increases. When the leakage
inductance becomes large, the coupling coefficient of thetransformer decreases. In addition, the resonance peak voltage
becomes large in comparison with the low Q. as a result, the ironloss becomes large. Thus, the resonance inductor loss reduction
is important in order to achieve the high efficiency. Therefore,
the improvement of the converter efficiency with the high Q
value has to be considered. This result is obtained with the half
bridge isolated DC/DC converter, and the conduction loss islarge because the transformer voltage becomes half. In order toimprove the efficiency, the full bridge isolated DC/DC converter
will be considered.
VI.

Fig. 12 Comparison between design value and experimental result. The
experimental result agrees with the design value.

100
98

Low Q value

96.5%

High Q value

93.6%

96
94
92
90

0

50

100

150
200
250
Output power [W]

300

350

Fig. 13 Efficiency characteristics with isolated DC/DC converter when Q
value is changed. In the high Q condition, the efficiency is reduced to93.6%. This is because the transformer loss is large.
Table.2 Simulation parameter

FUNDAMENTAL EVALUATION OF PROPOSED CIRCUIT

Table 2 shows the simulation condition. Fig.14 shows thesimulation result of the proposed circuit. According to fig. 14, it
is confirmed that the buffer capacitor voltage is fluctuated at thetwice grid frequency, and the input voltage ripple is under than
5% by controlling the buffer power pbuf. Thus, the operation of
the power ripple compensation is achieved. In addition, theoutput power factor is almost unity at the rated power, and theoutput current THD is 2.3%. From these results, it can be
confirmed that the proposed converter realizes the power
decoupling with the small capacitor Cbuf.
Fig. 15 shows the switching waveforms of the proposed
circuit. Each MOSFET of the active buffer and the CSI are also
switched at the zero current point by Δ−Σ_PDM. In addition, theisolated DC/DC converter achieves ZCS by the series resonance
operation as shown in fig. 11. It can be concluded from theseresults that, the switching losses is drastically reduced.
In order to further improve the efficiency, the transformer
design and the reduction of the conduction loss is importantbecause the proposed converter has many MOSFETs, and thetransformer losses such as the iron loss and the copper loss arelarge. The converter loss will be evaluated for high efficiency byexperiment.

VII. CONCLUSION
This paper presented the active power decoupling circuit
which is integrated to the CSI and the resonance type isolated
DC/DC converter. This converter compensated for the
instantaneous power fluctuation without the large electrolytic
capacitor. In addition, ZCS is achieved at the all switching
devices and the large inductor are not required because theleakage inductance of the transformer is used as a DC inductor.
The power decoupling with the small capacitor and the highfrequency operation was employed. Moreover, the clarification

of resonance parameter design for the proposed converter was
conducted. As a result, the experimental resonance current
peak is agrees with the design value with the error is less than
5%. In the proposed converter, the quality factor Q of the series
resonance should be designed to be high in order to maintain thestability of the resonance current. In this case, the reduction of
the resonance inductor loss is important in order to achieve thehigh efficiency. Finally, the fundamental operation of the
proposed converter was confirmed by simulation. As a result,the input voltage ripple was suppressed under than 5% by thepower decoupling control with small capacitor.
In the future work, the proposed converter operation will be
evaluated by the experiment. In addition, each loss and the highefficiency design will be considered.

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