For the digital control of systems such as gridconnected inverters, measuring inverter output currents accurately is essential. However, current measurement offsets are inevitably generated by current measurement paths and cause DC current components in real inverter output currents. Real inverter output currents with DC components cause the DClink capacitor voltage to oscillate at the frequency of a utility voltage. For these reasons, current measurement offsets deteriorate the overall system performance. A compensation strategy to eliminate the effect of current measurement offsets in gridconnected inverters is proposed in this study. The validity of the proposed compensation strategy is verified through simulations and experiments. Results show that the proposed compensation strategy improves the performance of gridconnected inverters.
I. INTRODUCTION
Environmental pollution and limited fossil fuel have prompted research into distributed generation systems using renewable energy sources (i.e., solar cells, fuel cells, or wind turbines)
[1]

[4]
. Power quality problems have also increased the demand for custom power devices
[5]

[7]
. These systems are usually operated by gridconnected inverters similar to those shown in
Fig. 1
. In gridconnected inverters, the precise control of inverter output currents must be achieved because electricity supply companies require adequate certification for harmonic distortion, power factor, and DC components for inverter output currents
[8

10]
. Accordingly, many methods for the current control of gridconnected inverters have been developed. These methods include the use of the stationary and synchronous frame proportionalintegral (PI) regulator
[11]
,
[12]
, stationary frame proportionalresonant (PR) regulator
[13]

[15]
, repetitivebased regulator
[16]
, deadbeat regulator
[17]
, and hysteresis regulator
[18]
.
Gridconnected inverters. (a) Singlephase gridconnected inverter. (b) Threephase gridconnected inverter.
However, the abovementioned studies do not consider current measurement offsets generated by the current measurement path. Generally, the procedure of current measurement is as follows. Inverter output currents are transduced to voltage signals by current sensors and transformed into digital values via lowpass filters and analogtodigital (A/D) converters. Through this current measurement path, current measurement offsets are inevitably generated and cause DC current components in real inverter output currents. Real inverter output currents with DC current components cause the DClink capacitor voltage to oscillate at the frequency of the utility voltage. This ripple distorts inverter output current references and deteriorates the overall system performance. This approach is called a firstorder ripple component in this study.
Calculating current offsets by reading the A/D converter repeatedly without current flowing is common practice. However, the effect of the thermal drift of analog devices and switching interference in actual operating conditions makes current offsets vary.
The distortion in inverter output current references caused by the firstorder ripple component can be prevented with a notch filter whose center frequency is equal to the frequency of utility voltages. However, the DC components of real inverter output currents injected into the utility side are not eliminated. The problem in DC current injection can be simply solved with a utility frequency transformer. However, this transformer increases the cost and size and reduces system efficiency. Bhat and Dewan
[19]
proposed a solution based on a highfrequency transformer to decrease the size. However, this solution does not prevent the DC current components of currents injected into the utility side. For these reasons, different solutions have been proposed to remove DC current components
[20]

[22]
, but these solutions require additional elements or sensors.
The solution proposed in this study does not require additional elements and sensors, except for sensors that are necessary to control gridconnected inverters. The proposed solution is thus very cheap and easy to implement. It is also applicable regardless of the topology of gridconnected inverters.
In this study, we analyze how current measurement offsets cause DC current components in real inverter output currents and the firstorder ripple component in the DClink capacitor voltage. A compensation strategy is proposed to eliminate DC current components in real inverter output currents and obtain precise current control.
The remainder of this paper is organized as follows. The effect of current measurement offsets is described in Section II. The proposed compensation strategy is introduced and discussed in Section III. The validity of the proposed strategy is verified by simulations and experiments in Sections IV and V. Finally, the conclusions are presented in Section VI.
II. EFFECT OF CURRENT MEASUREMENT OFFSETS
 A. Singlephase Gridconnected Inverters
Fig. 2
presents the block diagram of the current control in consideration of the measurement offsets of the utility voltage and output current in singlephase gridconnected inverters. In
Fig. 2
,
δv_{g}
and
δi_{g}
denote the measurement offsets in the utility voltage and the inverter output current, respectively, whereas
v_{g}
_
_{m}
and
i_{g}
_
_{m}
denote the measured utility voltage and inverter output current, respectively. On the assumption that the utility voltage is a complete sinusoidal wave as expressed in Equation (1), the inverter output current reference is expressed as Equation (2) so that active and reactive power may be regulated at the utility side, the pulse width modulation (PWM) is ideal, and the measurement offsets are constant. The inverter output current at the steady state in the current control using a proportionalintegralresonant (PIR) regulator (as expressed in Equation (3)) is expressed in Equation (4).
Block diagram of the current control in consideration of the measurement offsets in singlephase gridconnected inverters.
As Equation (4) shows, the current measurement offset causes the DC current component injected into the utility side in singlephase gridconnected inverters. At the steady state, using Equations (1) and (4) yields the inverter output voltage as follows:
If no power loss occurs in the inverter, the power supplied from the DClink to the inverter is similar to the inverter output power and can be expressed as Equation (6).
where
If the DClink capacitor voltage is maintained at the constant operating point (
V_{dc}
^{*}
), the power absorbed in the DClink capacitor can be obtained as follows:
Equation (7) shows that the current measurement offset causes the DClink capacitor voltage to oscillate at the utility voltage frequency in singlephase gridconnected inverters. This ripple deteriorates the overall system performance because it generates inverter output current reference with harmonics; thus, the real inverter output current also has harmonic components.
 B. Threephase Gridconnected Inverters
Fig. 3
presents the block diagram of the current control in consideration of the measurement offsets in threephase gridconnected inverters. In
Fig. 3
, (
δe_{d}^{s}
,
δe_{q}^{s}
) and (
δi_{d}^{s}
,
δi_{q}^{s}
) denote the stationary dqaxis measurement offsets of utility voltages and inverter output current, respectively, whereas (
e_{d}^{s}
_
_{m}
,
e_{q}^{s}
_
_{m}
) and (
i_{d}^{s}
_
_{m}
,
i_{q}^{s}
_
_{m}
) denote the stationary dqaxis measurement values of utility voltages and inverter output current, respectively. If the utility phase voltages are sinusoidalbalanced voltages, the stationary dqaxis voltages are expressed as Equation (8). The stationary dqaxis reference values of the inverter output phase current can be expressed as Equation (9) to control the active and reactive power at the utility side. Moreover, if the space vector pulse width modulation is ideal and the measurement offsets are constant, the stationary dqaxis output currents at the steady state in the current control system using a PIR regulator are expressed as Equation (10).
Block diagram of the current control in consideration of the measurement offsets in threephase gridconnected inverters.
Equation (10) shows that the current measurement offsets cause DC current components injected into the utility side in threephase gridconnected inverters. At the steady state, using Equations (8) and (10) yields stationary dqaxis inverter output voltages as follows:
If no power loss occurs in the inverter, the power supplied from the DClink to the inverter is similar to the inverter output power and can be expressed as Equation (12).
where
If the DClink capacitor voltage is maintained at the constant operating point (
V_{dc}
^{*}
), the power absorbed in the DClink capacitor can be obtained as follows:
Equation (13) shows that current measurement offsets cause the DClink capacitor voltage to oscillate at the utility voltage frequency in threephase gridconnected inverters. This ripple deteriorates the overall system performance because it generates inverter output current references with harmonics. Thus, real inverter output currents also have harmonic components.
III. DESIGN OF THE CURRENT OFFSET COMPENSATOR
 A. Singlephase Gridconnected Inverters
From Equation (7), the equation for the ripple component of the DClink capacitor voltage can be calculated as follows:
Equation (14) can be approximated as Equation (15) because the magnitude of the utility voltage is much larger than the impedance drop (
v_{g}
≫
ωL_{i} I_{d}^{e}
^{*}
,
ωL_{i} I_{q}^{e}
^{*}
).
As shown in Equation (15), the secondorder ripple component exists in singlephase gridconnected inverters. The band pass filter expressed in Equation (16) is used to detect the firstorder ripple component included in the current measurement offset.
where
BW
and
ω_{BPF}
are the bandwidth and the center frequency of the band pass filter, respectively. If
ω_{BPF}
is similar to the utility frequency, the firstorder ripple component can be obtained with
The firstorder ripple component expressed in Equation (17) is then filtered through the allpass filter expressed in Equation (18). When
ω_{APF}
is equal to the utility frequency, the allpass filter generates a virtual component expressed as Equation (19), which leads the firstorder ripple component by 90°.
By substituting Equations (17) and (19) into Equation (20), the magnitude of the firstorder ripple component can be established as Equation (21).
The current measurement offset can be calculated with Equation (21), but the real value cannot be determined without exact parameter values. Moreover, the current measurement offset may be altered by external factors. Hence, a current offset controller is used to maintain the calculated firstorder component at zero (
Fig. 4
).
Block diagram of a current offset controller in singlephase gridconnected inverters.
Fig. 5
presents the block diagram of a current control system using the proposed current offset compensator in singlephase gridconnected inverters. The current offset compensator is mainly composed of the firstorder ripple component detector, the magnitude detector, and the current offset controller. In
Fig. 5
,
i_{o}
_
_{com}
is a compensation value for the current measurement offset.
Block diagram of a current control system using the proposed current offset compensator in singlephase gridconnected inverters.
 B. Threephase gridconnected inverters
From Equation (13), the equation for the ripple component of the DClink capacitor voltage can be calculated as follows:
Equation (22) can be approximated as Equation (23) because the magnitude of the utility voltage is much larger than the impedance drop (
E
≫
ωL_{i} I_{d}^{e}
^{*}
,
ωL_{i} I_{q}^{e}
^{*}
).
Using the allpass filter expressed in Equation (18), the virtual component that leads the firstorder ripple component by 90° can be obtained as follows:
The magnitude of the daxis and qaxis voltage ripple can be obtained with Equation (26) by substituting Equations (23) and (24) into Equation (25).
Similar to singlephase gridconnected inverters, using a current offset controller (
Fig. 6
) is necessary.
Block diagram of a current offset controller in threephase gridconnected inverters.
Fig. 7
presents the block diagram of a current control system using the proposed current offset compensator in threephase gridconnected inverters. In
Fig. 7
,
i_{do}^{s}
_
_{com}
and
i_{qo}^{s}
_
_{com}
are stationary dqaxis compensation values for current measurement offsets.
Block diagram of a current control system using the proposed current offset compensator in threephase gridconnected inverters.
IV. SIMULATION RESULTS
Simulations and experiments were conducted with a sample distributed generation system (
Fig. 8
) to investigate the effect of offsets in gridconnected inverters and to verify the performance of the proposed current offset compensator. In the sample distributed generation system, a new renewable energy source was modeled as a DC voltage source. The detailed parameters are listed in
Table I
. In the case of singlephase gridconnected inverters, a secondorder voltage ripple that distorts the inverter output current inevitably exists in the DClink capacitor voltage. A notch filter whose center frequency is twice the utility frequency was utilized to eliminate the effect of the ripple component.
Sample distributed generation system for simulations and experiments.
PARAMETERS OF THE SAMPLE DISTRIBUTED GENERATION SYSTEM
PARAMETERS OF THE SAMPLE DISTRIBUTED GENERATION SYSTEM
Fig. 9
shows an output of the current offset compensator in singlephase gridconnected inverters. In the figure, the output of the current offset compensator converges at 1 A at the steady state to eliminate the effect of the current measurement offset.
Output of the current offset compensator in singlephase gridconnected inverters.
Fig. 10
shows the DClink capacitor voltage waveform in singlephase gridconnected inverters.
Fig. 10
(a) shows characteristics of transient and steady states before and after compensation.
Figs. 10
(b) and
10
(c) show the magnified waveform of the DClink capacitor voltage at the steady state before and after compensation, respectively. Comparison of
Figs. 10
(b) and
10
(c) shows that the firstorder ripple component disappeared after compensation, leaving only the secondorder ripple component. This scenario is an inherent characteristic of singlephase gridconnected inverters.
Fig. 10
shows that the DC component in the real inverter output current also disappeared.
DClink capacitor voltage in singlephase gridconnected inverters (a) before and after compensation of current measurement offset. (b) Steady state characteristic before compensation. (c) Steady state characteristic after compensation.
Fig. 11
shows the fast Fourier transform (FFT) analysis of the inverter output current at the steady state before and after compensation.
Fig. 11
(a) shows the DC and secondorder harmonic components before compensation. The secondorder harmonic component is caused by the firstorder ripple component of the DClink capacitor voltage. After compensation by the proposed method, the DC component and the secondorder harmonic of the inverter output current are almost eliminated as shown in
Fig. 11
(b).
FFT analysis result of inverter output current at the steady state in singlephase gridconnected inverters (a) before compensation and (b) after compensation.
Fig. 12
shows the output of the current offset compensator in threephase gridconnected inverters. Similar to singlephase gridconnected inverters, the current offset compensator calculates the compensation values at the steady state. The effect of the current measurement offset is thus eliminated.
Output of the current offset compensator in threephase gridconnected inverters.
Fig. 13
shows the DClink capacitor voltage waveform in threephase gridconnected inverters.
Fig. 13
(a) shows the characteristics of transient and steady states before and after compensation.
Figs. 13
(b) and
13
(c) show the magnified waveform of the DClink capacitor voltage at the steady state before and after compensation, respectively. Comparison of
Figs. 13
(b) and
13
(c) shows that the firstorder ripple component disappeared after compensation.
Fig. 13
shows that the DC component in the real inverter output currents also disappeared.
DClink capacitor voltage in threephase gridconnected inverters (a) before and after compensation of current measurement offset. (b) Steady state characteristic before compensation. (c) Steady state characteristic after compensation.
Fig. 14
shows the FFT analysis of the inverter output current at the steady state before and after compensation.
Fig. 14
(a) shows the DC and secondorder harmonic components before compensation. The secondorder harmonic component is caused by the firstorder ripple component of the DClink capacitor voltage. After compensation by the proposed method, the DC component and the secondorder harmonic of the inverter output current are almost eliminated as shown in
Fig. 14
(b).
FFT analysis result of inverter output current at the steady state in threephase gridconnected inverters (a) before compensation and (b) after compensation.
V. EXPERIMENTAL RESULTS
The configuration of the experimental system is shown in
Fig. 8
, and the parameters are listed in
Table 1
. TMS320F2812 was employed as a digital signal processor (DSP) in the experiment, and LA25NP was utilized as a current sensor. The range of the current input was designed to be between –15 A and 15 A. The transduced current signals were converted to digital values by 12bit A/D converters, and all internal data in the DSP were displayed on an oscilloscope through a 12bit D/A converter.
Fig. 15
shows the output of the current offset compensator in singlephase gridconnected inverters. The current measurement offset in the experiment is approximately –0.75 A. The result is similar to the simulation result in
Fig. 9
.
Output of the current offset compensator in singlephase gridconnected inverters.
The ripple component of the DClink capacitor voltage in singlephase gridconnected inverters before and after compensation is shown in
Fig. 16
. The figure also shows that the results similar to those of the simulation (
Fig. 10
).
Ripple component of DClink capacitor voltage in singlephase gridconnected inverters (a) before compensation and (b) after compensation.
An experiment for threephase gridconnected inverters was also performed. The output of the current offset compensator is shown in
Fig. 17
. The current measurement offsets of the experimental systems are approximately –0.3 A and 0.3 A in the stationary daxis and qaxis, respectively, similar to the simulation in
Fig. 12
.
Output of the current offset compensator in threephase gridconnected inverters.
Fig. 18
shows the ripple component of the DClink capacitor voltage in threephase gridconnected inverters. As shown in
Fig. 18
, the firstorder ripple component present before compensation is almost eliminated after compensation.
Ripple component of the DClink capacitor voltage in threephase gridconnected inverters (a) before compensation and (b) after compensation.
VI. CONCLUSIONS
In gridconnected inverters, current measurement offsets that are inevitably generated by the current measurement path cause DC current components in real inverter output currents. Real inverter output currents with DC components cause the DClink capacitor voltage to oscillate at the frequency of the utility voltage. In this study, a compensation strategy to eliminate the effect of these current measurement offsets was proposed. The validity of the strategy was demonstrated through both simulations and experiments. The experimental results show that the DC components disappeared from inverter output currents after compensation. By changing the current regulator, the proposed compensation strategy can be applied to inverter output current references that include harmonics components, although only the fundamental component was considered in this study. If DC voltage components exist in real utility voltages, the proposed compensation strategy eliminates DC current components in real inverter output currents. The proposed compensation strategy can thus improve the overall system performance of gridconnected inverters.
BIO
ChangHee Lee received his B.S. and M.S. degrees in electrical engineering from Kyungpook National University, Daegu, Korea, in 2008 and 2012, respectively. His current research interests include powerelectronic control of electric machines, systems that use renewable energy sources, and custom power devices.
JongWoo Choi received his B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1991, 1993, and 1996, respectively. He worked as a research engineer at LG Industrial Systems Company from 1996 to 2000. Since 2001, he has been a faculty member of the Department of Electrical Engineering, Kyungpook National University, Daegu, Korea, where he is currently a professor. His current research interests include static power conversion and electric machine drives.
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