Single phase grid connected PWM Inverter using PI controller

Abstract--Now a day’s distributed generation (DG) system
uses current regulated PWM voltage-source inverters (VSI) for
synchronizing the utility grid with DG source in order to meet
the following objectives: 1) To ensure grid stability 2) active and
reactive power control through voltage and frequency control 3)
power quality improvement (i.e. harmonic elimination) etc. In
this paper the comparative study between hysteresis and
proportional integral (PI) with hysteresis current controller is
presented for 1-Φ grid connected inverter system. The main
advantage of hysteresis+PI current controller is low total
harmonic distortion (THD) at the point of common coupling
(PCC) at a higher band width of the hysteresis band. The studied
system is modeled and simulated in the MATLAB Simulink
environment.
Index Terms-- Hysteresis current controller, PI controller, Point
of common coupling (PCC), DG, Utility grid, THD.
I. NOMENCLATURE
Vg grid voltage
Io grid current
Iref reference current
e current error
Vdc dc-link voltage
fs switching frequency
Lf line inductance
Vm maximum voltage amplitude
Im maximum current amplitude
θv voltage phase angle
θi current phase angle
II. INTRODUCTION
ISTRIBUTED generation (DG) systems becomes more
prominent in the world electricity market due to the
Satyaranjan Jena and Gokulananda Mishra are with the Department of
Electrical & Electronics Engineering, Hi-Tech Institute of Technology,
Khurda, Odisha-752057, India (Email:srj.nitrkl@gmail.com)
B.chittibabu is with the Department of Electrical Engineering, National
Institute of Technology, Rourkela, Odisha-769008, India
Amiya Ku. Naik is with the Department of Electrical Engineering,
Sudargarh Engineering College, Sundargarh, Odisha, India
978-1-4673-0136-7/11/$26.00 ©2011 IEEE
increased demand for electric power generation. The
deregulation of the electric power industry and to reduce the
greenhouse gas emissions etc.
Distributed generation systems and their interconnection
should meet certain requirements and specifications when
interconnecting with existing electric power systems (EPS)
[1]. For an inverter-based distributed generator, the power
quality largely depends on the inverter controller’s
performance. Pulse width modulation (PWM) is the most
popular control technique for grid-connected inverters. As
compared with the open loop voltage PWM converters, the
current-controlled PWM has several advantages such as fast
dynamic response, inherent over-current protection, good dc-
link utilization, peak current protection etc [2].
For quick current controllability, unconditioned stability,
good current tracking accuracy and easy implementation, the
hysteresis band current control (HBCC) technique has the
highest rate among other current control methods such as
sinusoidal PWM [3-4]. However, the bandwidth of the
hysteresis current controller determines the allowable current
shaping error. By changing the bandwidth, the user can
control the average switching frequency of the grid connected
inverter and evaluate the performance for different values of
hysteresis bandwidth. In principle, increasing the inverter
operating frequency helps to get a better compensating current
waveform. However, there are device limitations and
increasing the switching frequency causes increasing
switching losses, audible noise and EMI related problems. [5]
The main aim of this study is to investigate the effects of
hysteresis bandwidth on the THD of supply current of grid
connected inverter. Hysteresis+PI current controller
minimizes the current error up to a certain limit even if the
bandwidth of the hysteresis band is more. The advantage of
conventional PI controller is it reduces the steady state error to
zero and is very simple to implement.
The paper is organized as follows – Current control
strategies in grid connected system are given in Section II.
Single-phase grid connected VSI is described in Section III.
Analysis of hysteresis and adaptive current controller is
explained in the section. Section V dedicated to results and
discussion, followed by conclusion in Section VI and
references in section VII.
Performance Improvement of Single-Phase Grid
–Connected PWM Inverter Using PI with
Hysteresis Current Controller
Satyaranjan Jena Member, IEEE, and B.Chitti Babu, Member IEEE,
Amiya Kumar Naik, Gokulananda Mishra
D

III. SINGLE PHASE GRID-CONNECTED VSI
Grid-connected inverter is the core component of the
distributed generation system. It can be broadly classified into
two categories: inverters with isolating transformer and
inverters without it, where the former one offer better EMI
capability than transformer less inverters.
A current controlled VSI is generally used to synchronize
the utility grid with the distributed generation as shown in
Fig.1.With advances in modern power semiconductor
technology fast switching devices such as IGBT’s and IGCT’s
are widely used as switches in inverter circuits.
Fig.1. Single phase grid- connected VSI
The single-phase grid connected inverter shown in Fig.1 is
composed of a dc voltage source (VDC), four switches (S1-S4),
a filter inductor (Lf) and utility grid (Vg). In inverter-based
DG, the produced voltage from inverter must be higher than
the Vg. It is required to assure power flow to grid. Since Vg is
uncontrollable, the only way of controlling the operation of
the system is by controlling the current that is following into
the grid.
IV. ANALYSIS OF HYSTERESIS AND HYSTERESIS + PI CURRENT
CONTROLLER
A. Reference Current Computation
Here the reference signal is calculated Using Torrey and
Al-Zalmel [6] methodology. First, the grid voltage is sensed
and adjusted to a desired value before converting it to current
signal to become the reference current signal which is given in
the equation (1).
ref s
i kv
= (1)
Where Vs is the source voltage and k is a scaling factor.
Such computation depends on the amount of power being
demanded by the load. Hence, k must be frequently updated in
order to compensate for the variations of the load current. The
control scheme updating interval is a line voltage cycle period
and the scaling factor is computed as
2
2 L
m
P
k
V
= (2)
Where
1
1
( ) ( )
n
L s L
j
P v j i j
n =
= ∑ (3)
Where Vs is the source voltage, iL is the load current, and n
is the number of voltage and current samples taken during one
cycle period of the source voltage. For sinusoidal voltage and
current signals, the average power is expressed as
cos( )
2
m m
v i
V I
P θ θ
= − (4)
Where Vm is the voltage amplitude, Im is the current
amplitude, θv is the voltage phase angle, and θi is the current
phase angle. Under unity power factor conditions, the current
amplitude is
2
m
m
P
I
V
= (5)
B. Hysteresis band current controller.
Hysteresis current control is one of the easiest control
methods to implement. It is simple to implement and has
robust current control performance against load and source
parameter changes [7]. Hysteresis current control is a method
of controlling a voltage source inverter where the measured
current is compared to reference current on instantaneous
basis. The current error is then compared directly against a
predefined band called hysteresis band to produce switching
pulses for the voltage source inverter. This method controls
the switches in an inverter asynchronously to ramp the current
through an inductor up and down so that it tracks a reference
current signal.
Fig.2. Hysteresis –Band Current Controller
By notice equation (6) the reference line current of the grid
connected inverter is referred to as iref , measured line current
of the grid connected inverter is referred to as io and difference
between io and iref is referred to as e. The hysteresis band
current controller assigns the switching pattern of grid
connected inverter.
o ref
e i i
= − (6)
The switching logic is formulated as follows:
If e >HB then switch S1 and S4 is on
If e <-HB switch S2 and S3 is on
C. The hysteresis+PI band current controller
The main drawback of hysteresis current controller is
uneven switching frequency which causes acoustic noise and
In case of hysteresis+PI as shown in the Fig.3. The error
signal e is processed by PI controller before feeding to the
hysteresis band. The grid inductance and resistance is treated
as the plant for the PI controller. difficulty in designing input

filters. The switching frequency can be reduced by reducing
the band width of the hysteresis band but at the same time the
current error will increase which produce more distortion in
the output current.
Fig.3. Block diagram for hysteresis current control of single-phase grid-
connected VSI
The PI controller is very simple to implement and also it
reduces the steady state error to zero. By using PI we can add
the advantage of PI to hysteresis controller to make the system
more robust [8].
Fig.4. Hysteresis –Modulator
In this case the grid voltage is sensed and adjusted to a
desired value before converting it to current signal to become
the reference current signal. This will ensure the current
produced by inverter-based DG is in phase with grid voltage
and also achieve unity power factor. This method is robust and
effective than conventional reference signal generation by the
controller and matching it with the grid voltage at later stage.
This method also reduces the number of components such as
Phase Lock Loop (PLL) circuits and cost [9-10].
From Fig.3
o
dc f g
di
V L V
dt
= + (7)
From equation (1)
o ref
i i e
= + (8)
Hence
( )
ref
dc f g
d i e
V L V
dt
+
= + (9)
By rearranging equation (4)
( )
ref
dc g f
d i e
V V L
dt
+
− = (10)
For dynamic condition:
dc g f
de
V V L
dt
− = (11)
So perturbation error can be written as:
dc g
f
V V
de
dt L
−
= (12)
During the interval when switches S1 and S4 is ON (TON
time), the error current changes from –HB to +HB. Thus, the
ON time can be calculated as:
2 f
ON
dc g
L HB
T
V V
=
−
(13)
By using a similar method, the interval when switches S2
and S3 receive ON signals (TOFF time) can be obtained as
2 f
OFF
dc g
L HB
T
V V
=
+
(14)
( )( )
4 dc f
s ON OFF
dc g dc g
V L HB
T T T
V V V V
= + =
+ −
(15)
Thus, the switching frequency is:
( )( )
1
4
dc g dc g
s
s dc f
V V V V
f
T V L HB
+ −
= = (16)
( )
2 2
4
dc g
s
dc f
V V
f
V L HB
−
= (17)
Hence, the switching frequency varies with the dc input
voltage, grid voltage, load inductance and the hysteresis band.
V. RESULTS & DISCUSSION
The section reveals the simulation results for hysteresis and
hysteresis with PI current control algorithm applied to single-
phase mains connected inverter system. The studied model has
been developed and simulated in the MATLAB/simulink
environment. For simulation, the Dc-link voltage is taken
400V, and the grid voltage is 240V, the inductance of the line
is 5mH and the utility grid frequency is 50Hz.
A. Simulation result for fixed band width (HB=constant)
Fig.5and 6 shows response of hysteresis and hysteresis
with PI current controller for constant band width of the
hysteresis band.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-200
0
200
a
-V
o
lta
g
e
(V
)
b
-C
u
rre
n
t(A
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-20
0
20
C
u
re
n
t(A
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
1
2
3
4
5
x 10
4
Time(Sec)
F
rq
u
e
n
c
y
(H
z
)
Io e
a
b
Iref
Fig.5. Simulation result of the hysteresis current controller for fixed
band (a) grid voltage (Vg) and grid current (Io) (b) reference
current, actual current and current error(c) switching frequency
In case hysteresis controller the distortion in the grid
current and the current error is more as compared to
hysteresis+PI controller which is shown in fig 5(b)&6(b)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-200
0
200
a
-V
o
lta
g
e
(V
)
b
-C
u
rre
n
t(A
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-20
0
20
C
u
rre
n
t(A
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
1
2
3
4
5
x 10
4
Time(Sec)
F
re
q
u
e
n
c
y
(H
z
)
e
Iref
Io
a b
Fig.6. Simulation result of the hysteresis+PI current controller for fixed
band (a) grid voltage (Vg) and grid current (Io) (b) reference
current, actual current and current error(c) switching frequency
B. Simulation result for step change in hysteresis band width
To analyze the performance of the hysteresis and
hysteresis+PI controller the band width of the hysteresis band
is changed during the simulation period.
Fig.7 (a) shows that the distortion in the grid current
increases as the band width increases in case of hysteresis
controller, in the other hand the distortion in hysteresis+PI
controller is negligible with variation of band as shown in
Fig.8(a).
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-20
0
20
C
u
rre
n
t(A
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
1
2
3
4
5
x 10
4
F
re
q
u
e
n
c
y
(H
z
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-10
0
10
Time(Sec)
C
u
rre
n
t(A
)
HB=1 HB=3 HB=5
HB=1 HB=3 HB=5
HB=1 HB=3 HB=5
Fig.7. Simulation result of hysteresis current controller for change in
band (a) grid current (b) switching frequency(c) current error
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-20
0
20
C
u
r
r
e
n
t
(
A
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
2
4
x10
4
F
r
e
q
u
e
n
c
y
(
H
z
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-2
0
2
Time(Sec)
C
u
r
r
e
n
t
(
A
)
HB=1 HB=3 HB=5
HB=1 HB=3 HB=5
HB=1 HB=3 HB=5
Fig.8. Simulation result of hysteresis+PI current controller for change in
band (a) grid current (b) switching frequency(c) current error
Fig 8(b) and 8(c) implies that the switching frequency can
be decreased by increasing the band width without any change
in current error for hysteresis+PI controller. But the same is
not possible in conventional hysteresis controller which is
obvious from Fig 7(b) and 7(c). Finally, the current harmonic
spectrum for hysteresis and hysteresis+PI controller for
different band width is given in a tabular form (Table-1).Fig 9
and 10 shows the THD of the grid current for both the
controller with different band width. From the result we can
conclude that the increase in THD of the grid current is

negligible in hysteresis+PI controller as compared to
hysteresis controller.
Fig.9. THD of grid current for hysteresis current controller
(a) HB=1(b)HB=3(c)HB=5
Fig.10. THD of grid current for hysteresis+PI current controller
(a) HB=1(b) HB=3(c) HB=5
VI. CONCLUSIONS
From the study we observed that, hysteresis+PI current
controller can enable to reduce switching frequency even if
the band width increased without any significant increase in
the current error. Hence it provides considerably less THD at
higher band width as compared to conventional hysteresis
current controller.
VII. REFERENCES
[1] Blaabjerg, F.; Teodorescu, R.; Liserre, M.; Timbus, A.V., “Overview of
Control and Grid Synchronization for Distributed Power Generation
Systems” IEEE Transactions on Industrial Electronics,Vol.:53 ,
Issue:5, Page(s): 1398 – 1409, 2006
[2] F.Blaabjerg, Zhe Chen, and S.B. Kjaer. “Power Electronics as Efficient
Interface in Dispersed Power Generation Systems”, IEEE Transactions
on Power Electronics, 19(5):1184–1194, Sept. 2004.
[3] Ho, C.N.-M.,Cheung, V.S.P.,Chung, H.S.-H.” Constant-Frequency
Hysteresis Current Control of Grid-Connected VSI without Bandwidth
Control”,IEEE Trans. on Power Electronics, TPEL 2009,Volume: 24,
no. 11 ,, Pp:2484 – 2495, 2009
[4] Rahman, M.A.; Radwan, T.S.; Osheiba, A.M.; Lashine, A.E.; “Analysis
of Current Controllers for Voltage-Source Inverter” IEEE Trans. on
Industrial Electronics, Volume: 44 , no. 4 , Pp. 477 – 485, ,1997
[5] Tekwani, P.N, Kanchan, R.S., Gopakumar, K.; “Current-error space-
vector-based hysteresis PWM controller for three-level voltage source
inverter fed drives” Proceedings of Electric Power Applications, IEE
Volume: 152 , Issue: 5, Pp: 1283 – 1295,2005
[6] D. Torrey and A. Al-Zamel, "Single-phase active power filters for
multiple nonlinear loads," IEEE Transactions on Power Electronics,
vol. 10, no. 3, pp. 263-272, May 1995.
[7] M.P.Kazmierkowaski, L.Malesani: “PWM Current Control Techniques
of voltage source converters-A Survey” IEEE. Trans. On Industrial
Electronics, Vol.45, no.5, pp.691-703, Oct.1998.
[8] Habeebullah Sait H, Arul Daniel S. New control paradigm for
integration of photovoltaic energy sources with utility network. Int J
Electr Power Energ Syst (2010), doi:10.1016/j.ijepes.2010.08.002.
[9] Krismadinata,Rahim N.A.,Selvaraj,J.,” Implementation of Hysteresis
Current Control for Single-Phase Grid Connected Inverter”Inter. Conf.
on Power Electronics and Drive Systems,.PEDS '07., pp: 1097 – 1101,
2007
[10] Xunjiang DAI, Qin CHAO “The Research of Photovoltaic Grid-
Connected Inverter Based on Adaptive Current Hysteresis Band Control
Scheme” inter. National conf. on sustainable power generation and
supply,SUPERGEN,09. Page(s): 1 – 8, 2009

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