1

Power Control of Single-Phase

Voltage Source Inverter for Grid-Connected
Photovoltaic Systems
S. Samerchur, S. Premrudeepreechacharn, Member, IEEE, Y. Kumsuwun, and K. Higuchi, Member, IEEE

and both injected active and reactive powers are controlled. In

Abstract-- This paper presents the design and analysis of both [5], hysteresis current control and sensorless MPPT for grid-
the active and reactive power control of a single-phase voltage connected photovoltaic system application have been
source inverter (VSI) for grid-connected photovoltaic (PV) presented. These control methods provide robust current
system. The proposed method is based on vector control of power
regulation, unity power factor, low THD and optimize the
by decoupling control of the active and reactive current
components to feed the active and reactive power to the grid. The energy suitable for grid-connected. However, it has major
aim of this research is to control power factor at grid, to improve drawback in variable switching frequency, current error of
overall efficiency of transferring power of PV to alternate twice the hysteresis band, and high-frequency limit-cycle
current power conversion into the grid, and to decrease phase operation [6]-[9].
current distortion of VSI. In this work, mathematical model of This paper presents a power control of a single-phase
system has presented in details. The results of simulations of PV voltage source inverter for grid-connected photovoltaic
system 1kW connected to grid 220V, 50 Hz using
system. The proposed method is based on vector control of
MATLAB/Simulink software are also discussed. Simulation
results have shown that the grid input power factor is nearly power by decoupling control of the active and reactive current
unity, and the distorting of phase current of the proposed system components to feed the active and reactive power to the grid.
has been reduced, causing the total harmonic distortion for The aim of this research is to control power at grid, to
various power conditions falls within 5%. improve overall efficiency of transferring power of PV to
alternate current power conversion into the grid, and to
I. INTRODUCTION decrease phase current distortion of VSI.

R enewable energy source such as photovoltaic, hydro, and The paper is organized as follows. The grid-connected
wind generation systems have received much attention photovoltaic system is analyzed in Section II. Then, the single
recently as alternative means of generating electricity. The phase vector control system is described in Section III. Next,
photovoltaic systems are used today in many applications. It the simulation results are discussed in Section IV. Finally, the
has the advantage of being maintenance and pollution free [1], conclusion is discussed in Section V.
[2]. Photovoltaic system that supplies power directly to the
utility grid is becoming more popular due to cost reduction. II. GRID-CONNECTED PHOTOVOLTAIC SYSTEM
The aim of grid-connected photovoltaic energy converter is to This section describes the operation of grid-connected
process the power and inject a sinusoidal current into the photovoltaic system, analysis of the single-phase voltage
utility grid [3], [4]. source inverter for designing proposed decoupled control
A digital control strategy for a single-phase inverter (VSI) system. In addition, it describes relation between real power
based on the phase shift between the inverter output voltage and reactive power which are controlled from real and
and the grid voltage with the digital sinusoidal pulse width reactive current components.
modulation patterns is proposed in [4]. The advantage of this
control strategy is implementation very simple digital circuits, A. Operation of Grid-Connected Photovoltaic System
The configuration of a single-phase grid-connected
Authors would like to thank the financial supports from Thailand Research photovoltaic system is shown in Fig. 1. It consists of
Fund Master Research Grants (TRF-MAG) and National Research University photovoltaic array, a DC-DC boost converter, input and
Project from Office of the Higher Education Commission of Thailand and the output capacitor, single-phase VSI, filter inductor, and supply
University of Electro-Communication.
S. Samerchur is with Department of Electrical Engineering, Chiang Mai
voltage. The PV arrays are connected to a DC-DC boost
University, Chiang Mai, Thailand (e-mail: supansa.cmu@gmail.com). converter for step up the PV voltage to the level of the
S. Premrudeepreechacharn is with Department of Electrical Engineering, allowable maximum line voltage. The single-phase VSI with
Chiang Mai University, Chiang Mai, Thailand (e-mail: suttic@eng.cmu.ac.th).
filter inductor converts a DC input voltage into an ac voltage
Y. Kumsuwun is with Department of Electrical Engineering, Chiang Mai
University, Chiang Mai, Thailand (e-mail: yuttana@ee.eng.cmu.ac.th). by means of appropriate switch signals to make the output
K. Higuchi is with Department of Electrical Engineering, the University of current in phase with utility voltage and unity power factor. A
Electro-Communications, Tokyo, Japan (e-mail: higuchi@ee.uec.ac.jp). typical controller configuration of the single-phase grid-

978-1-61284-788-7/11/$26.00 ©2011 IEEE

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connected photovoltaic system consists of a maximum power

point tracking (MPPT) controller, single-phase vector B. Analysis of Single-Phase VSI for Grid-Connected
controller. The MPPT controller is achieved through a current Photovoltaic System
estimator of the PV array, and generates the reference voltage
for the DC-DC boost converter. This converter controls the The single-phase vector control scheme allows independent
PV voltage to constant DC-link voltage. The single-phase controllability for the active and reactive power of grid-
vector controller controls the line current for unity power connected photovoltaic system. The objective of the single-
factor [10]. phase VSI is based on the decoupled vector control concept,
to maintain a constant ac-link voltage value, and to feed active
power into the grid. This control scheme transforms to the
v
fundamental output voltage of inverter vo1 and supply voltage
v
vs into the real and imagines voltage components in the
stationary reference frame α − β , as follow:
v
vo1 = voα 1 + jvoβ 1 (1)
v
vs = vsα + jvsβ (2)

where voα 1 , voβ 1 are the fundamental output voltage

Fig. 1. The configuration of grid-connected photovoltaic system. components of the inverter in the stationary reference
frame α − β , and vsα , vsβ are the supply voltage components
The maximum power point characteristic of solar panel is
in the stationary reference frame α − β .
shown in Fig. 2. The model of PV array was implementing,
and typical parameter for 120W module was used to plot V-I
curve for various irradiation levels at 25 oC. The photovoltaic The equivalent circuit of the single-phase VSI for grid-
system is composed of 10 solar panels connected in series. connected system is shown in Fig 3 (a). In order to illustrate
The parameter of solar panel is described in Table I. the circuit characteristic, Fig 3 (b) is represented the phasor
v v
diagram for the supply voltage vs , the output current io , the
I (pu.) v
fundamental output voltage of the inverter vo , and the
v
MPP Region inductance voltage vL . The phase different between the supply
1000 W/m2 v v
1.0 voltage vs and the output current io is represented as φ ,
MPP Line
800 W/m2 displacement power factor (DPF).
0.8

600 W/m2
0.6

400 W/m2
0.4
200 W/m2
0.2

V (pu.)
0 0.2 0.4 0.6 0.8 1.0
(a) (b)
Fig. 2. Photovoltaic array characteristic.
Fig. 3. Equivalent circuit and phasor diagram of the proposed method.
TABLE I
THE CHARACTERISTICS OF PHOTOVOLTAIC PANEL The equivalent circuit, phasor diagram and voltage vector in
(1) and (2) can be written voltage equation in the stationary
Mitsubishi, PV-MF 120 EA, 1000 W/m2, AM 1.5, 25 oC
reference frame α − β with Kirchhoff’s voltage law (KVL) as
Maximum power ( Pmax ) 120 W follows:
Open-circuit voltage ( Voc ) 23 V
Short-circuit current ( I sc )
⎡ voα 1 ⎤ ⎡ioα ⎤ d ⎡ioα ⎤ ⎡ vsα ⎤
6.89 A
⎢ v ⎥ = R ⎢i ⎥ + L ⎢i ⎥ + ⎢ v ⎥ (3)
⎣ oβ 1 ⎦ ⎣ oβ ⎦ dt ⎣ oβ ⎦ ⎣ sβ ⎦
Maximum power voltage ( Vmp ) 19 V

Maximum power current ( I mp ) 6.30 A

where ioα , ioβ are the output current components of the
inverter in the stationary reference frame α − β , and L, R are
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the inductance and parasitic resistance of inductance, The supply voltage and output current of inverter can be
respectively. expressed as:
v
From (3), the voltage equation in the stationary reference vs = Vˆs cos (ωst ) (5)
frame α − β can be transforming into the rotating reference
v
frame d − q , can be expressed as: io = Iˆo cos (ωst − φ ) = Iˆod cos (ωst ) − jIˆoq sin (ωst ) (6)

⎡vod 1 ⎤ ⎡iod ⎤ d ⎡iod ⎤ ⎡ 0 −ωs L ⎤ ⎡iod ⎤ ⎡vsd ⎤ From (6), the output current components of inverter in the
⎢ v ⎥ = R ⎢i ⎥ + L ⎢i ⎥ + ⎢ ⎢ ⎥+⎢ ⎥ (4) rotating reference frame d − q can be expressed as:
⎣ oq1 ⎦ ⎣ oq ⎦ dt ⎣ oq ⎦ ⎣ωs L 0 ⎥⎦ ⎣ ioq ⎦ ⎣ vsq ⎦

where vod 1 , voq1 are the fundamental output voltage iod = Iˆo cos ( −φ ) = Iˆo cos (φ )
(7)
components of the inverter in the rotating reference
ioq = Iˆo sin ( −φ ) = − Iˆo sin (φ )
frame d − q , and vsd , vsq are the supply voltage components in
the rotating reference frame d − q , iod , ioq are the output
where Vˆs , Iˆo are the maximum supply voltage and output
current components of the inverter in the rotating reference
frame d − q , and ωs is electrical frequency of grid voltage, current of inverter, Iˆod , Iˆoq are the maximum output current
ωs = 2π f s (rad/s). components of inverter in the rotating reference frame d − q .

Equation (4) shows the relationship between the Considering (5)-(7), the active and reactive powers of grid-
fundamental output voltage of the inverter and supply voltage connected can be calculated by:
in the rotating reference frame d − q . Hence, the equivalent
circuit in this frame is shown in Fig. 4. It is seen that the Vˆ Iˆ
p = Vˆs cos (ωst ) ⋅ Iˆod cos (ωst ) = s ⋅ o cos (φ )
d − q axis voltages are cross coupled by term −ωs Lioq and 2 2
(8)
1
ωs Liod , respectively. = vsd iod
2

Vˆs Iˆo
q = −Vˆs cos (ωs t ) ⋅ Iˆoq sin (ωst ) = − ⋅ sin (φ )
2 2
(9)
1
= − vsd ioq
2

From (8) and (9), the control of the active and reactive
power flow to grid is performed by the inverter. The active
power is predominantly dependent on the real current
component iod , while reactive power is dependent on the
imagines current component ioq .
Fig. 4. Equivalent circuit of the proposed method in the rotating reference
frame d − q . III. SINGLE-PHASE VECTOR CONTROL SYSTEM
Considering (4) in Section II for the decoupled vector
C. Active and Reactive Power of Single-Phase System control, the d − q axis equations compensation terms are
introduced be defining:
Fig. 5 shows the phasor diagram of the supply voltage and
output current in rotating reference frame d − q for calculated vod 1 = vLd
'
+ (ωs Lioq + vsd )
the active and reactive powers in system. (10)
voq1 = vLq
'
− (ωs Liod )
q-axis s= st
where
iod
d-axis
vs = vsd diod
'
vLd = Riod + L
dt
(11)
-ioq dioq
io
'
vLq = Rioq + L
dt
Fig. 5. Phasor diagram of voltage and current in rotating reference frame
These equations are rearranged with relations to current
d −q. components, when expressed in the s -domain with s = d / dt .
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This reveals the electrical transfer functions G ( s ) as seen in TABLE II

THE SIMULATION PARAMETERS OF SYSTEM
(12).
Grid voltage ( vs ) 220 Vrms

iod ( s ) ioq ( s ) 1 Frequency ( fs ) 50 Hz

G (s) = = = (12)
v '
Ld (s) v '
Lq (s) R + Ls Switching frequency ( f sw ) 5 kHz

DC-link capacitance ( Cdc ) 2,400 μF

In order to make the output currents track the reference
current, the PI current control is used to determine the demand Inductance ( L ) 12 mH
values for vLd'
and vLq'
. The outputs of the decoupled axis Parasitic resistance of the inductance ( R ) 0.05 Ω
reference voltages control are expressed as follows:
DC-link voltage ( Vdc ) 440 V

v*
od 1 = v + (ωs Lioq + vsd )
'
Ld
(13) DC bus voltage is always kept constant by boost converter
1 = vLq − ( ω s Liod )
* '
voq using maximum power tracking controller in any isolations
level between 200 W/m2 to 1,000 W/m2. The single phase
Finally, the strategy for the decoupled single-phase vector inverter is operated in PWM unipolar mode with switching
control of the inverter for grid-connected photovoltaic system frequency 5 kHz. The output of single phase inverter is used
is shown in Fig. 7. This control scheme has three control inductor as harmonic filter to connect to grid. The simulation
loops. The output power and power factor of the grid can be results can be discussed as follows.
controlled via changing the current components. In (14), the
DC reference voltages ( vod* , voq* ) is converted to the AC A. Steady state operation
reference voltages ( vo*α , vo*β ) form, which the output voltage of
In Fig. 7, the voltage and the current waveforms are
the controller in α -axis ( vo*α ) is used to generate the PWM represented in steady-state conditions. The objective is
signals for switching the devices in the single-phase inverter. extracting the maximum power of PV and feeding 1,000 W
active power to the grid-connected. Fig. 7 (a) shows the
⎡ vo*α ⎤ ⎡ cos (θ s ) sin (θ s ) ⎤ ⎡vod *
⎤ steady-state waveforms of the DC-link voltage vdc , the output
⎢ * ⎥=⎢ ⎥⎢ * ⎥ (14)
⎣⎢voβ ⎦⎥ ⎣ − sin (θ s ) cos (θ s ) ⎦ ⎣⎢ voq ⎦⎥ voltage vo , the supply voltage vs , and the output current is . As
expected. The output current injected into the grid is exactly
in phase agreement with the supply voltage. Fig. 7 (b) shows
IV. SIMULATION RESULTS the steady-state waveforms of output current components
To verify the performance of the proposed the control of a ids , iqs and active and reactive power p, q . As it is shown,
single-phase VSI for grid-connected photovoltaic system, active and reactive powers are independently controllable
represented in the block diagram in Fig. 6, has been which powers were 1000 W and 0 VAr, respectively. There
implemented considering a single-phase VSI as represented in are consistence with current command of iod and ioq which are
Fig. 1. The parameters used in the simulation system are
6.43 A and 0 A, respectively. As seen from simulation results,
described in Table II.
the proposed decoupled vector control can control power
feeding into the grid with stability. In Fig. 8, the frequency
spectrum of output voltage and current of inverter are shown,
where the supply voltage and output current are in phase and
at unity power factor. Total harmonic distortions (THD) of
current and voltage are 4.80% and 86.89%, respectively. The
power factor is improved to DPF/ 1 + THD i2 = 0.998 .

Fig. 6. Block diagram of vector control in the proposed method.

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reactive current reference control with active power flowing

from the supply into the DC-link. The setting of reactive
vdc
current reference iqs* is stepped from +3.2 A to -3.2 A at 50
vo ms. In Fig. 9 (a), it can be seen that the output current of
inverter can operated under the lagging and leading power
(a) io factor condition with the performance of the DC-link voltage
constant at 440 V. Fig. 9 (b) shown the dynamic response
vs waveforms of output current components ids , iqs and active
and reactive powers p, q . It is seen that the active power was
constant at 1,000 W and the reactive power was stepped
« 10ms/div 200V/div, 6.67A/div change from 500 VAr to -500 VAr at 50 ms.

iod
ioq vdc
vo
(b)
p (a) io
q vs

« 10ms/div 10A/div, 1000W/div, 1000VAr/div

0ms 20ms 40ms 60ms 80ms 100ms « 10ms/div 200V/div, 6.67A/div

Fig. 7. Voltage, current, active and reactive owers during steady state
operation..
iod
*
ioq ioq

Iˆo (%) (b) p

« 10ms/div 10A/div, 1000W/div, 1000VAr/div

0ms 20ms 40ms 60ms 80ms 100ms

Fig. 9. Voltage, current, and active and reactive power waveforms during
Vˆo (%) dynamic step changes.

C. Supplied nonlinear load

Finally, Fig. 10 shows the simulation results when the

Frequency (x10 kHz) nonlinear load is supplied through the inverter. The simulated
has been demonstrated using a nonlinear load which is 87 W
Fig. 8. Frequency spectrum waveforms of output current and voltage during (250 W) resistive through a half-bridge rectifier. The setting
stead state operation.
of the load is stepped from with load to without load at 65 ms.
B. Dynamic operation Fig. 10 (top) shows the supply voltage and output current of
the inverter. It can be seen that the output current is in phase
The proposed configuration, operating in dynamic response, with the supply voltage and the unity power factor
the power factor of the single-phase VSI for grid-connected transmission to the grid is achieved. Fig. 10 (middle) shows
photovoltaic system can be controlled by adjusting the the voltage and current of the nonlinear load. The current
reference of the reactive current iqs* . As can be seen from Fig. exhibits a standard half-bridge rectifier waveform that THDi
of 43.61%. Fig. 10 (bottom) depicts the supply voltage and the
9, the dynamic response of the inverter to a step changed in
 6

supply current when the system supplies the nonlinear load. It Reactive Power Compensation,” IEEE Transactions on Energy
Conversion, Vol. 22, Issue 4, Dec. 2007, pp. 881-886.
can be seen that the waveform the magnitude of supply [9] E. Roman, R. Alonso, P. Ibanez, S. Elorduizapatarietxe, and D. Goitia,
current is changed according to the available power feeding to “Intelligent PV module for grid-connected PV systems,” IEEE
grid. In the meantime, the current is still kept in phase with Transaction Industrial Electronics, Vol. 53, Issue 4, Jun. 2006, pp. 1066-
voltage to get unity power factor. 1073.
[10] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of
With load Without load control and grid synchronization for distributed power generation
systems,” IEEE Transactions on Industrial Electronics, Vol. 53, Issue 5,
Oct. 2006, pp. 1398-1409.
vs
VII. BIOGRAPHIES
io
Supansa Samerchur received the B.S. degree in
industrial education from King Mongkut's
Institute of Technology Ladkrabang (KMITL),
Bangkok, Thailand, in 2005. She is currently
vload studying toward his M.Eng. degree in Electrical
Engineering at Chiang Mai University. Her
iload research interests are in power electronics and
renewable energy system.

vs
Suttichai Premrudeepreechacharn received the
B.Eng. degree in electrical engineering from
is Chiang Mai University, Chiang Mai, Thailand, in
1988 and the M.S. and Ph.D. degree in electric
« 10ms 200V/div, 6.67A/div power engineering from Rensselaer Polytechnic
Institute, Troy, NY, in 1992 and 1997,
0ms 20ms 40ms 60ms 80ms 100ms
respectively. Currently, he is an Associate
Professor with the Department of Electrical
Engineering, Chiang Mai University. His
Fig. 10. Voltage and current waveforms when supply to nonlinear load. research interests include power electronics,
electric drives, power quality, high-quality utility
interfaces and articial-intelligence-applied power
V. CONCLUSIONS
system.
This paper has proposed a control strategy of vector control
for the grid-connected single-phase VSI in the photovoltaic Yuttana Kumsuwan received the M.Eng. degree
in electrical engineering from King Mongkut's
system. The objective of the grid-connected inverter control is
Institute of Technology Ladkrabang (KMITL),
to maintain the DC-link voltage and independent active and Bangkok, Thailand, in 2001. and the Ph.D.
reactive power flow. The simulations results have shown that degree in electrical engineering from the Chiang
this strategy is able to have a good dynamic responses and Mai University, Chiang Mai, Thailand, in 2007.
He is a lecture in the Department of Electrical
high accuracy to the active and reactive power control. Engineering, Chiang Mai University, His
research interests are in power electronics, high
VI. REFERENCES power converters and electric drives.

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