IEEE PEDS 2017, Honolulu, USA
12 – 15 December 2017

Mixed Conduction Mode Control for Inductor
Minimization in Grid-Tied Inverter
Hoai Nam Le, Jun-ichi Itoh
Nagaoka University of Technology
1603-1 Kamitomioka Town
Nagaoka City, Niigata Prefecture, Japan
Tel.: +81 / (258) – 47.9533.
E-Mail: lehoainam@stn.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/index.html
Abstract— This paper proposes a mixed-conduction-mode(MCM) current control for a grid-tied inverter operating inboth continuous current mode (CCM) and discontinuous current mode (DCM) in order to minimize an interconnected inductor. In general, a low interconnected inductor value worsens disturbance suppression of current controller, and leads toan increase in grid current total harmonic distortion (THD). In
DCM, the disturbance-to-current transfer function becomes
nonlinear and the disturbances such as the dead time voltage
error are effectively suppressed. Therefore, the grid-tied inverter operating in MCM can achieve a low grid current THD.
However, another DCM nonlinearity occurs in the duty-tocurrent transfer function, which makes control gain characteristic in DCM completely different from that in CCM. Therefore, the DCM nonlinearity compensation is proposed by using
duty at previous calculation. The validity of the proposed current control is confirmed with a 1-kW 100-kHz prototype.
Even when using the interconnected inductor with a normalized impedance of 0.16%, the grid current THD is reduced
from 14.8% to 2.9% at rated load compared to the conventional CCM control. Furthermore, the inductor volume is reducedby 77.0%, whereas the converter loss is reduced by 36.5%.
Keywords—Single-phase grid-tied inverter, Continuous
current mode, Discontinuous current mode, Mixed conductionmode, Disturbance compensation.

I

I. INTRODUCTION

N recent years, researches on photovoltaic system(PV) has attracted many attentions due to the increasing demand of renewable resources [1]-[3]. H-bridge
inverters are usually used in the PV system in order to convert DC power from solar panel into AC power in the conventional AC single-phase grid. In such grid-tied inverters,
LCL filters are generally employed between the inverter andthe grid in order to suppress current harmonics and meet gridcurrent harmonic constraints as defined by standards such as
IEEE-519-1992 [4]-[5]. This LCL filter, especially the interconnected inductor, accounts for a majority of the inverter
volume [6]-[7]. By increasing switching frequency and reducing an inductor value, the interconnected inductor volume can be minimized. However, the grid-tied inverter generally operates in CCM, where the disturbance suppression
performance worsens with the reduced inductor value. This
leads to the increase in the grid current THD. In order toovercome this problem, a disturbance observer which is designed based on CCM transfer function is utilized. The disturbance observer can suppress the disturbance effects on thecurrent control and allows the reduction of the inductor value. Nevertheless, this method requires high speed controllers
such as, e.g. field-programmable gate array (FPGA), in orderto estimate the rapidly-changing disturbances, e.g. the deadtime error voltage [8].
As another approach, the disturbance effects can be reduced by DCM. The zero-current interval in DCM introduces the nonlinearity into the disturbance-to-current transfer
function, which effectively suppresses the disturbance effects
such as the dead time voltage error. However, another nonlinearity occurs in the duty-to-current transfer function,
which makes the current control gain in DCM completely
different from that of CCM [9]-[10]. A nonlinearity compensation has been proposed and effectively achieves the current
command response as same as CCM [10]. Nevertheless, theproposed DCM current controller can be applied only in
DCM, which implies that the grid-tied inverter has to operatein DCM over entire load range. This design significantly
increases conduction loss of switching devices due to highcurrent ripple of DCM at rated load. Therefore, many control
methods which allow the inverter to operate in both CCM
and DCM have been proposed to improve the conversion
efficiency [11]-[14]. However, these MCM control method
becomes dependent on the inductor value, which decays therobustness of the controller against the change of the inductor value [15].
This paper proposes a novel MCM current control for the
grid-tied inverter operating in both CCM and DCM. The
DCM nonlinearity in the disturbance characteristic is used toreduce the grid current THD, whereas the DCM nonlinearity
in the duty-to-current transfer function is compensated byusing the duty at the previous calculation period. Meanwhile,the current mode determination between CCM and DCM is
accomplished by comparing the DCM duty and the CCM
duty at the output of the controller. Thank to this method, thecurrent feedback control is independent of the inductor value
and can operate at any load condition. This paper is organized as follows: first the problems with the increasing gridcurrent THD when the inductor value is reduced in CCM
operation is explained. Next, two DCM nonlinearities are

978-1-5090-2364-6/17/$31.00 ©2017 IEEE

investigated when the power factor is lower than one in orderto stably operate the grid-tied inverter at any load condition.
Then the MCM current control for both CCM and DCM is
proposed in order to obtain the low grid current THD withthe small inductor value. Finally, the effectiveness of the
proposed current control is confirmed experimentally with a
1-kW prototype. The comparisons of the grid current THD
and the conversion efficiency are demonstrated.

Grid side| Gdis _ CCM |

1
L n

1
2

 2   2  ....... (1),4 2  n2 1  2 
  n 

where L is the inverter-side inductor value,  is the disturbance angular frequency,  and  n are the damping factor andthe angular frequency of the current controller, respectively.
Fig. 3 depicts the gain of the disturbance response in
CCM under different conditions of L. Because |Gdis_CCM| isinversely proportional to L, the disturbance effects increase
10 times when L is reduced from 1 p.u. to 0.1 p.u.. Consequently, this worsens the disturbance response. In general,
when the typical dead-time error voltage compensation isapplied with the high L, the current distortion is effectively
reduced. However, when L is greatly reduced, only a small
mismatch between the estimated and actual dead-time error
voltage (vdeadtime_est and vdeadtime) which is caused by such as
the current detection delay, results in a high current distortion due to the greatly-increasing gain of the disturbance
response |Gdis_CCM|. Note that by increasing the angular frequency of the current controller  n, the gain of the disturbance response |Gdis_CCM| can be reduced, i.e. the current distortion can be reduced. However, a high bandwidth current
control requires a high speed controller, which is an undesired solution.

Lg

ig

iout

vg

Cf

SW1

SW2

Fig. 1. Single-phase H-bridge grid-tied inverter with LCL filter. A singlephase H-bridge inverter is applied due to its simplicity, which is important for stability analysis and reliability design.

PI Controller

Control System Circuitvg
vg

Kp(sTi+1)
sTi

1 D1
Vdc

iout_avg*
iout_avg

sign

VdcTd fsw

Vdc

vdis

vdeadtime
1 iout_avg
sL

vdeadtime_est
e-sT

Fig. 2. Conventional CCM feedback current control block with typicaldead-time error voltage compensation. When the interconnected inductor
is minimized by reducing the inductor value, the inverter become more
vulnerable to the disturbances, i.e. the increase in the disturbance gain.
Disturbance response gain |Gdis_CCM| [dB]Fig. 2 indicates the conventional CCM feedback current
control block with a typical dead-time error voltage compensation. Note that the grid current ig and the grid voltage vg areassumed to be as same as iout and the voltage vCf across thefilter capacitor Cf, respectively, because the cutoff frequencyof the LCL filter is designed to be much higher than the
bandwidth of the current control loop. The amplitude of the
disturbance-voltage-to-current transfer function in CCM
which is also entitled the gain of the disturbance response|Gdis_CCM| is derived from Fig. 2 and expressed as in

Lf

L

Vdc

II. PROPOSED MIXED CONDUCTION MODE CURRENTCONTROL
A. Current Distortion in Conventional Continuous Current
Mode Control
Fig. 1 indicates the circuit configuration of the singlephase grid-tied inverter. In this paper, a single-phase Hbridge inverter is applied due to its simplicity. The LCL filter
connects the inverter to the grid in order to suppress the current harmonics of the inverter output current iout. Note thatthe grid has its own intrinsic inductor Lg, the value is different depending on the type and the condition of the grid.

SW2

SW1

20
0

Low impedance L of 0.1 p.u.
Increase 20 dB (10 times)

-20
-40
-60
High impedance L of 1.0 p.u.

-80

1.0 p.u. equals 5% of the total inverter impedance.

-100
0.1

1

10
100
1000
Disturbance frequency f [Hz]10000

100000Fig. 3. Disturbance response gain in CCM. The minimization of theinductors in CCM is limited by the increase in the disturbance gain.

B. Compensation of Discontinuous-Current-ModeNonlinearity in Duty-To-Current Transfer Function
Fig. 4 indicates the grid-tied inverter operation under different conditions of the power factor. Fig. 4(a), (b) shows therelationship between the grid voltage vg and the output current iout of the inverter at the unity power factor and the power factor below one, respectively. Meanwhile, Fig. 4(c), (d)depicts the inverter operation mode and the output current
waveform when the inverter operates in powering mode atinterval ii in Fig. 4(b) and generation mode at interval i in
Fig. 4(b), respectively. Note that the grid-tied inverter is operated in bipolar modulation in order to reduce common current, whereas the grid-side inductors Lg, Lf, and the filter
capacitor Cf are omitted due to the simplification. As shownin Fig. 4(a), the inverter operates in only the powering mode
when the power factor is unity. On the other hand, the in-

vg

vg
iout

iout
0

0

Intervals:

ii

iv

vg>0
iout>0vg * iout >0
Powering

vg<0
iout<0vg * iout >0
Powering

Intervals: ivg>0
iout<0vg * iout <0Generation(a) Grid voltage and output current at unity power factor
Mode 1

Inductor
currentiout
0iMode 1Mode 2

L

L

L

L

iout

iout

iout

iout

Vg

Vdc

Current peak
ipeak

D1Tsw

iv
vg<0
iout<0vg * iout >0
Powering(b) Grid voltage and output current at power factor below one

Mode 2

Vdc

ii
iii
vg>0
vg<0
iout>0iout>0vg * iout >0 vg * iout <0Powering Generation

D2Tsw
Tsw

Vg

Averagecurrent
iavg

D3Tsw

Vdc

Vg

D1Tsw

Vdc

D2Tsw
Tsw

Vg

D3Tsw

0
Inductor current
iout

Average current iavg
Current peak ipeak(c) Inverter operation mode and output current waveform(d) Inverter operation mode and output current waveformin powering mode (cf. interval ii of Fig. 4(b))
in generation mode (cf. interval i of Fig. 4(b))
Fig. 4. Grid-tied inverter operation under different conditions of power factor. Different from the CCM operation, the inverter operation mode in DCM depends on the relationship between the grid voltage vg and the output current iout of the inverter, i.e. the powering mode or the generation mode. This is because
the zero-current interval introduces nonlinearities into the DCM operation.

verter alternatively operates in the powering mode and thegeneration mode when the power factor is below one asshown in Fig. 4(b). Consequently, as shown in Fig. 4(c), (d),the applying order of mode 1 and mode 2 in the poweringmode is flipped compared to that in the generation mode.
The reason is that different from the CCM operation, theinverter operation mode in DCM depends on the relationshipbetween the grid voltage vg and the output current iout of theinverter, i.e. the powering mode or the generation mode.
Therefore, in order to control the grid-tied inverter in DCM,
the circuit model has to be analyzed in each the poweringmode and the generation mode. For the sake of brevity, only
the operation in the powering mode is discussed in the following. However, the operation in the generation mode isderived analogously.
Considering the inverter operation and the output current
waveform in the power mode shown in Fig. 4(c) (cf. the interval ii in Fig. 4(b)), D1, D2 and D3 denote the duties of thefirst, the second and the zero-current interval. The equation
based on the average model of the inverter shown in Fig. 4(c)is given by (2) [9]-[10],VL  D1 (Vdc  Vg )  D2 (Vdc  Vg ) ......................... (2)where VL is the average inductor voltage, Vdc is the DC-link
voltage and Vg is the grid voltage. The average current iavg
and the current peak ipeak, which are shown in Fig. 4(c) are
expressed as,iavg 

i peak( D1  D2 ) .......................................... (3)2
Vdc  Vgi peak 
D1Tsw ......................................... (4)L
where Tsw is the switching period. Substituting (4) into (3)and solving the equation for the duty D2. The duty D2 is expressed by

D2 

2 Liavg
D1Tsw (Vdc  Vac ) D1 ............................... (5),Substituting (5) into (2) in order to remove the duty D2 andrepresent (2) as a function of only the duty D1, then (6) isobtained.

D1
[0~1]

VL

Vdc

2

1
sL

iavg

iavg*

Nonlinear factor

Do notexist in
CCM

1
iavg
0.5ipeak(Vdc-Vg)Tsw
2L

0.5ipeakPIiavg

Vdc + Vg
D3

z-1
z

a
Vdc + |vg|
2Vdc(Vdc - |vg|)
b

z-1
z

a/b

D1

x2

|x|

z-1

(i) Compensation for nonlinearity in grid-voltage-to-current transfer function(a) Proposed DCM current control for powering mode

iavg

iavg*

PI
iavg

V*L

a
Vdc - |vg|
2Vdc(Vdc + |vg|)
b

a/b

D1

2Vdc2
(Vdc - |vg|)2
z-1
z

vg

z-1
z

(ii) Compensation for nonlinearity in
duty-to-current transfer function

Conventional CCM
PI Controller

Δvg

ΔD1

V*L

2Vdc2
(Vdc + |vg|)2
vg

Fig. 5. Circuit model of inverter operated in DCM at powering mode. In
DCM, the current control depends greatly on the current value, i.e. thenonlinearities occurring in the duty-ratio-to-current transfer function andthe disturbance-to-current transfer function.

(i) Nonlinearity in
grid-voltage-to-current
transfer function(ii) Compensation for nonlinearity in
duty-to-current transfer function

Conventional CCM
PI Controller

Vg

1

x2

|x|

z-1

(i) Compensation for nonlinearity in grid-voltage-to-current transfer function(b) Proposed DCM current control for generation mode
2Vdc_s2D1_s2(Vdc_s + Vg_s)22Vdc_sD1_s(Vdc_s - Vg_s)
Vdc_s + Vg_s

VL

Conventional CCM
PI Controller

Tsw
L(z-1)

Δiavg(ii) Nonlinearity in duty-to-current transfer function

Fig. 6. Discretized circuit model in DCM at powering mode. The originalidea of the DCM nonlinearity compensation is to estimate the duty atsteady states by the duty at the previous calculation. Consequently, theinductor value is not required in the DCM nonlinearity compensation.


2 Liavg
VL  Vdc (2 D1  1)  Vg  (Vdc  Vg )1  (Vdc  Vg ) D1Tsw .............................................................................. (6)Then, the inverter model in DCM is established based on (6).
Fig. 5 illustrates the circuit model of the inverter operating in DCM at powering mode which is based on (6). In
CCM, the dash line part does not exist, because the average
current iavg equals to the half current peak ipeak/2. On the other words, this makes the zero-current interval D3Tsw shown in
Fig. 3 become zero. However, in DCM, the zero-current interval introduces the nonlinearities into the DCM transfer
function. The design of the compensation part for the DCM
nonlinearity is explained as in [10]. The circuit model in Fig.
5 is linearized and discretized at steady state points.
Fig. 6 depicts the discretized circuit model at poweringmode. Note that Vdc_s, Vg_s, and D1_s are the DC-link voltage,
the grid voltage and the duty at steady state points, whereasvg, D1, and iavg are the small signals of the grid voltage,
the duty and the average current, respectively. The zerocurrent interval introduces nonlinearities in the grid-voltageto-current transfer function and the duty-to-current transfer
function.
Fig. 7 (a)-(c) indicates the proposed DCM current controls for the powering mode, for the generation mode and for

iavg*

PI
iavg

V*L

(ii) Compensation for nonlinearity in
duty-to-current transfer functiona
Vdc + vgsign(iavg*)
2Vdc[Vdc - vgsign(iavg*)]
b

D1

a/b

2Vdc2
[Vdc + vgsign(iavg*)]2
vg

z-1
z

x2

|x|

z-1

(i) Compensation for nonlinearity in grid-voltage-to-current transfer function(c) Proposed DCM current control for any condition of power factor
Fig. 7. Proposed DCM current control for any conditions of power factor.
By using the information of the output current polarity, the proposed
DCM nonlinearity compensation can be employed over entire range ofthe power factor.

any conditions of the power factor, respectively. As shown in
Fig. 7(a), in order to compensate the DCM nonlinearities atthe output of the PI controller designed in CCM, the nonlinearity in the duty-to-current transfer function in Fig. 6 is set as
1, whereas the nonlinearity in the grid-voltage-to-current
transfer function is eliminated by feeding forward the gridvoltage to the output of the PI controller. In principle, thecurrent control in Fig. 7(b) is the same as that in Fig. 7(a).
However, the sign of the absolute value of the grid voltage in
Fig. 7(b) is opposite to that in Fig. 7(a), because as shown in
Fig. 5(c), (d), the applying order of mode 1 and mode 2 inthe powering mode is flipped compared to that in the generation mode. In order to control the DCM current under any
conditions of the power factor, the combination of the current control from Fig. 7(a) and (b) is required. By using theinformation of the output current polarity, the proposed
DCM nonlinearity compensation can be employed over entire range of the power factor.
Fig. 8 shows the gain of the disturbance response in
CCM and DCM under different conditions of the steadystate duty-ratio D1_s. In CCM, the minimization of the inductor value L worsens the disturbance response. On the otherDisturbance response gain [dB]

hand, in DCM when the steady-state duty-ratio D1_s becomes
smaller, the disturbance response gain in DCM decreases.
The reason is that the proposed DCM nonlinearity compensation for the current command response does not compensate for the DCM nonlinearity in the disturbance response.
Consequently, the disturbance response depends on thesteady-state duty-ratio D1_s. Therefore, by utilizing this nonlinearity characteristic in which the disturbance gain decreases greatly with the small steady-state duty-ratio D1_s, i.e.
the interval near the current zero-crossing point or the light
load, the current distortion can be reduced.
0
-10
-20
-30
-40
-50
-60
-70
-80

Grid-connected Inductance L: 150 mH
DC-link Voltage Vdc: 380 V
Grid Voltage Vg_s: 141 V

CCM

D1_s = 0.3

DCM

C. Current Mode Determination
Fig. 9 shows the relationship among the CCM duty, theDCM duty and the current mode. In conventional current
mode determination, the average current (the detection value
iavg or the command value iavg*) is compared with the current
value IBCM at the boundary between CCM and DCM, whichis calculated by using the inductor value. Consequently,
when the actual inductor value is different from the nominal
value, the current mode cannot be accurately determined by
the conventional method. On the other hand, the proposedcurrent mode determination focuses on the relationship between the CCM duty and the DCM duty when the current
mode alternates. In particular, when the circuit operates in
DCM, the DCM duty becomes smaller than the CCM duty
and vice versa. Therefore, using this relationship, the proposed current mode determination is achieved without using
the inductor value. This makes the MCM controller robust
against the change of the inductor value.

D1_s = 0.1

Fig. 10 indicates the proposed MCM current control andthe waveform of the current mode alternation. The CCM
duty DutyCCM is calculated without using the inductor value.
Similarly, the inductor value is unnecessary in the calculation of the DCM duty DutyDCM, because the inductor value is
not used in the DCM nonlinearity compensation. Consequently, the relationship between the CCM duty and the
DCM duty which is independent from the inductor value isachieved. Thank to this, the proposed MCM current control
can be applied even when the inductors with high tolerance
are used.

D1_s = 0.05

10

100
1000
Disturbance frequency f [Hz]Fig. 8. Disturbance characteristics in CCM and DCM. The DCM nonlinearity in the disturbance-to-current transfer function makes the DCM
current more resistant to the disturbance than the CCM current. Therefore, the interconnected inductor can be further minimized in DCM.

0.6

DCM
DDCM＜DCCM
Mode transition point

Duty ratio

0.5
0.4

CCM
DDCM≧DCCM
DDCM

0.2

Table I depicts the experimental parameters. The operation frequency of the current controller is synchronized withthe sampling frequency of 20 kHz despite of the high switching frequency of 100 kHz, which enables the use of low
speed controllers.

Inductor current value atBoundary Mode
IBCM

0.1
0

III. LABORATORY SETUP

DCCM

0.3

0

0.5

1
1.5
2
2.5
Inductor Current [A]Fig. 9. Relationship among CCM duty, DCM duty and current mode.
When the circuit operates in DCM, the DCM duty becomes smaller thanthe CCM duty and vice versa. Using this relationship, the current mode
determination is achieved without using the inductor value.
DCM Duty Generation
iavg*
iavg

PI

V*L
2Vdc2

Vdc + vgsign(iavg*)a2Vdc[Vdc - vgsign(iavg*)]b

Current mode alternation

Current Mode Determination
Duty

a/b
DutyDCM|x|[Vdc + vgsign(iavg*)]2
z-1
vg
z

x2

|x|

NOT

z-1

DutyCCM0.5
0.5sign(iavg*)

CCM Duty Generation

SW1

iout
iavg

0A
-1

|x|
1
Vdc

vg

Fig. 11 depicts the prototypes of the inverter-side inductors L under different conditions of the inductor impedance%ZL normalized by the based impedance. Ferrite is chosen

SW2

1
0
0

Duty
DutyDCM

DutyCCM

Fig. 10. Proposed MCM current control for grid-tied inverter operating under any condition of power factor. The proposed
MCM current control is independent from the inductor value because the inductor value is not used in both the DCM nonlinearity compensation and the current mode determination.

TABLE ISYSTEM PARAMETERS.

0V

Circuit Parameter

Grid Voltage vg (500 V/div)

VDC
DC link Voltage
380 Vvg
Grid Voltage
200 Vrms
Pn
Nominal Power
1 kW
Switching Device (SiC MOSFET) SCH2080KE
Core material and Litz wire
Ferrite N87, 100/f0.1
fg
Grid Frequency
50 Hz
Zb
Base Impedance
40 W
Cb
Base Capacitance
79.6 mF
Cf
Filter Capacitor
0.5 mF
fsw
Switching Frequency 100 kHz
Current Controller Parameter
fsamp
Sampling Frequency
20 kHzDamping Factor
1.4
fc
1 kHz
Cutoff Frequency

Grid Current ig (10 A/div)

0A
0A
Inverter-side-inductor Current iout (10 A/div)
Time (10 ms/div)(a) Conventional CCM current control with %ZL = 3.1% at rated load

0V
Grid Voltage vg (500 V/div)

Grid Current ig (10 A/div)

THDig=6.8%

0A
0A

L(%ZL=3.1%)
VolL=110cm3(1.0p.u.)

Inverter-side-inductor Current iout (10 A/div)
L(%ZL=0.6%)
VolL=52cm3(0.47p.u.)

THDig=1.5%

Time (10 ms/div)(b) Conventional CCM current control with %ZL = 0.6% at rated load

w = 35 mm

w = 29 mm

w = 19 mm

l = 55 mm

l = 42 mm

l = 36 mm

h = 37 mm

h = 43 mm

h = 57 mm

L(%ZL=0.16%)
VolL=25cm3(0.23p.u.)

Fig. 11. Prototypes of inverter-side inductors under different conditionsof inductor impedance normalized by base impedance. By reducing theimpedance of the inverter-side inductor %ZL from 3.1% to 0.16%, theinductor volume is reduced by 77%.

to be the core material in order to minimize the core loss atthe switching frequency of 100 kHz, whereas Litz wire isused in order to minimize the winding loss coming from theproximity effect and the skin effect. By the application of
DCM, the normalize impedance of the inductor impedance%ZL can be minimized without worsening the disturbance
response as shown in Fig. 8. Consequently, by reducing theimpedance of the inverter-side inductor %ZL from 3.1% to0.16%, the inductor volume is reduced by 77%.
Fig. 12 and Fig. 13 shows the grid voltage, the grid current and the inverter output current of the conventional CCM
current control and the proposed MCM current control at
rated load of 1kW and at light load of 200W, respectively.
The IEEE-519-1992 standards require the grid current THD
below 5% at rated load, which can be accomplished simply
with the high impedance of the inverter-side inductor %ZL asshown in Fig. 12 (a). However, as L is reduced to minimize
the interconnected inductor, the disturbance effects in CCM
increase with small %ZL as shown in Fig. 3. Consequently,
the grid current THD increases from 1.5% to 14.8%
when %ZL is reduced from 3.1% to 0.16%. This problem canbe overcome by increasing the control bandwidth of the current controller, which is difficult to employ with low speed
microprocessors. On the other hand, when the inverter isoperated in MCM, the disturbance effects naturally reduce at
low duties as shown in Fig. 8, i.e. the zero-crossing intervals,

0V
Grid Voltage vg (500 V/div) Grid Current ig (10 A/div)

THDig=14.8%

0A
0A

Inverter-side-inductor Current iout (10 A/div)
Time (10 ms/div)(c) Conventional CCM current control with %ZL = 0.16% at rated load

0V
Grid Voltage vg (500 V/div) Grid Current ig (10 A/div)

THDig=2.9%

0A
0A
DCM CCM DCM
Inverter-side-inductor Current iout (10 A/div)

Time (10 ms/div)(d) Proposed MCM current control with %ZL = 0.16% at rated load
Fig. 12. Grid voltage, grid current and inverter output current of conventional CCM current control and proposed MCM current control at rated
load of 1kW. When the inverter is operated in MCM, the disturbance effects naturally reduce at low duties, i.e. the zero-crossing intervals, due tothe nonlinearity in the disturbance response.

due to the nonlinearity in the disturbance response. Therefore,
the low grid-current THD of 2.9% is achieved with the proposed MCM current control even when %ZL is reduced to
0.16%. Similarly, the grid current THD at light load of 200W
is also reduced from 27.6% to 2.5%.
Fig. 14 shows the comparison of the grid current THD
and the conversion efficiency between the conventional
CCM current control and the proposed MCM current control
with different of normalized impedances. Even when thenormalized impedance of the grid-side inductor %ZL is min-

Conventional CCM control with
%ZL=3.1%
35.1%ZL=0.6%%ZL=0.16%
Proposed MCM control with
%ZL=0.16%

40

Grid Voltage vg (500 V/div)

Grid Current ig (2 A/div)

THDig=2.1%

0A
0A
Inverter-side-inductor Current iout (2 A/div)

Time (10 ms/div)(a) Conventional CCM current control with %ZL = 3.1% at light load
0V
Grid Voltage vg (500 V/div)

Grid Current ig (2 A/div)

Grid Current Distortion THDig [%]

0V

30

27.6

25

23.1
17.8

20

14.8

15

10.5

10

9.7

5
2.1

THDig=10.5%

0A

35

0

2.5

Current distortion reduced by 80.4%
8.7
7.7
6.8

4

2

3.6
1.8

3.4
1.6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Output Power Pout [p.u.](a) Grid current THD characteristics
0

0A
Inverter-side-inductor Current iout (2 A/div)

98

Time (10 ms/div)

0V
Grid Voltage vg (500 V/div) Grid Current ig (2 A/div)

THDig=27.6%

0A

Conversion Efficiency h [%](b) Conventional CCM current control with %ZL = 0.6% at light load

Grid Voltage vg (500 V/div)

Grid Current ig (2 A/div)

THDig=2.5%

0A

1.1

97
96
95
Conventional CCM control with
%ZL=3.1%%ZL=0.6%%ZL=0.16%
Proposed MCM control with
%ZL=0.16%

94
93
92

0V

1.5
1

Loss reduced by 36.5%

0A

Inverter-side-inductor Current iout (2 A/div)
Time (10 ms/div)(c) Conventional CCM current control with %ZL = 0.16% at light load

2.90

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Output Power Pout [p.u.](b) Conversion efficiency characteristics
Fig. 14. Comparison of grid current THD and conversion efficiency between conventional CCM current control and proposed MCM current
control with different of normalized impedances. The trade-off relationship between the grid current THD and the efficiency occurs in the conventional CCM current control, whereas the proposed MCM control canachieve both the low grid current THD and the high efficiency.

occurs in the conventional CCM current control, whereas the
proposed MCM control can achieve both the low grid current
THD and the high efficiency.

0A
Inverter-side-inductor Current iout (2 A/div)

Time (10 ms/div)(d) Proposed MCM current control with %ZL = 0.16% at light load
Fig. 13. Grid voltage, grid current and inverter output current of conventional CCM current control and proposed MCM current control at lightload of 200W.

imized to 0.16% of the inverter total impedance, the gridcurrent THD is maintained to be lower than 5% over entire
load range by applying the proposed MCM current control.
Furthermore, by minimizing %ZL to 0.16%, the efficiency isimproved by 1.5% compared with the normalized impedance
of %ZL=3.1%. Furthermore, in the conventional CCM current control, the lower the grid THD becomes, the higher theconversion loss becomes. On the other words, the trade-off
relationship between the grid current THD and the efficiency

Fig. 15 depicts the proposed MCM current control operation at the rated current and under different power factors.
The low grid current THD can still be achieved at low power
factor with the proposed MCM current control. On the otherwords, the proposed MCM current control provides the gridtied inverter the capability of fault-ride-through. The effectiveness of the proposed MCM current control is confirmedby these experimental results.
IV. CONCLUSION
When the grid-connected inductor is minimized by reducing the inductor impedance, the disturbance effects increases highly in the CCM operation, which distorts the gridcurrent. On the other hand, in the DCM operation, the non-

Grid Voltage vg (250 V/div)

Grid Current ig (10 A/div)

THDig=2.8%

0V
0A

The main contribution of this paper is that the proposed
MCM current control is independent from the inductor value because the inductor value is not used in both the DCM
nonlinearity compensation and the current mode determination.
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0A
Inverter-side-inductor Current iout (10 A/div)

Time (10 ms/div)(a) MCM current control operation at power factor of 0.95
Grid Voltage vg (250 V/div)

Grid Current ig (10 A/div)

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0V
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0A
Inverter-side-inductor Current iout (10 A/div)

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0V
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Inverter-side-inductor Current iout (10 A/div)

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