Three phase grid connected inverter using current

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 2, March – April (2013), © IAEME
293
THREE-PHASE GRID-CONNECTED INVERTER USING CURRENT
REGULATOR
Tran Quang Tho, Truong Viet Anh
Faculty of Electrical & Electronic Engineering,
HCM City University of Technical Education
ABSTRACT
This paper presents an approach for a three-phase grid-connected inverter using
current regulator. The switching frequency of hystereris in the current modulation is fixed by
comparing the current error with carrier wave with the constant frequency of the multiple of
3. The LCL filter is installed at the inverter output to offer high harmonic attenuation. In
order to determine simply the parameters of PI regulators, the methods of PSO, GA and the
conventional Ziegler-Nichols are used to search the best values with high global stability. The
simulation results in Simulink/Matlab show that the PI regulators designed by PSO method
demonstrate better results than Ziegler-Nichols and even GA technique.
Keywords: gen algorithm (GA), particle swarm optimization (PSO)
I. INTRODUCTION
The demand of renewable energy sources such as solar energy is becoming more
popular for sustainability and environment with enormous potentials [1]. In order to convert
solar DC source to three-phase AC power needs to have 3-phase inverters that have been well
researched in recent years [2].
The current modulation plays an important role in power electronic systems,
especially in voltage source inverters [3]. The advantages of current regulator are very
simple, fast response, high robust and overload protection. In addition, it also keeps power
factor unity and does not depend on voltage drop of switches [15]. However, the hysteresis
PWM has unfixed switching frequency that increases loss of switches and current THD [16].
The elimination of common mode voltage in VSIs aims to reduce THD by using
compensation circuitry [4], harmonic filters [5], [6], [7] and carrier wave phase shift [8] is
very complicated. In order to meet grid-connected standard IEEE Std 929-2000 [9] with
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING
& TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 4, Issue 2, March – April (2013), pp. 293-304
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2013): 5.5028 (Calculated by GISI)
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IJEET
© I A E M E

294
harmonic attenuation [10], LCL filter is installed at inverter output. The simulation results
discussed show that the PI regulators designed by PSO demonstrate better results than
Ziegler-Nichols and even GA method.
II. MODEL OF GRID-CONNECTED THREE PHASE INVERTER AND CONTROL
STRATEGY
The principle diagram of grid-connected three phase system is shown in Fig 1.
Fig 1: Simplified model of the grid-connected inverter with L filter
II.1. Current regulation
The three phase AC quantities Ia, Ib and Ic in the stationary frame are transformed into
the DC components Id and Iq in the synchronously rotating frame by the phase angle Θ of
PLL. With L filter in grid-connected VSI as Fig 1, voltage equation of phase A in the
stationary frame is:
)1(ViRV
dt
di
L gaagia
a
−−=
And phases B and C are similar. When neglecting resistor Rg, equation (1) became:
)2(VV
dt
di
L gaia
a
−=
The equation (2) shows that phase current can be regulated by amplitude and phase angle
of Vi at inverter output with constant Vg as Fig 2.
Fig 2: Relationship between Vi and Ig in dq frame

295
Active and reactive powers in dq frame are calculated as (3) and (4).
( )
( ) )4(IVIV
2
3
Q
)3(IVIV
2
3
P
gqgdgdgq
gqgqgdgd
−=
+=
With reference P_ref and Q_ref, currents Idp and Iq can determine as:
( ) )5(
V
V
PQ
QP
VV3
2
I
I
gq
gd
ref_ref_
ref_ref_
2
gq
2
gdq
dp
















−+
=








The current Idp depends on DC source power status of solar. So:
)6(PP dcref =
For optimization of generation, only active power is to be injected in the grid and
reference Iq is zero. Pdc and Idp can be determined by MPPT technique. To obtain the closed
loop response, Id and Iq are taken from the outputs of the inner loop PI regulator, as (7).
Where Id and Iq are the reference currents. Kp and Ki are the proportional and integral gain
constants respectively. These gain constants are determined by tuning the regulators for
optimal response with methods of Ziegler-Nichols, GA and PSO.
)7(
II
II
s
K
K0
0
s
K
K
I
I
qgref_q
dgref_d
iq_i
iq_p
id_i
id_p
*
q
*
d








−
−












+
+
=








The LCL filter of the inverter output is proposed as Fig 3.
Fig 3: The proposed diagram of three phase inverter with LCL filter

296
II.2. DC link voltage control
The DC voltage is held at a constant value by using a PI regulator which provides the
real current reference as (8). Where V*dc is the DC voltage of MPPT.
[ ] )8(VV
s
K
KII dc
*
dc
dc_i
dc_pdpref_d −





+−=
II.3. PWM modulation
Current error: )9(III gref_gerror_ −=
Then:
( ) )10(VV
dt
Id
L iref_i
error_
−=
Current errors are compared with carrier wave of fixed frequency and amplitude. If
the current error is positive and larger than the carrier wave, the switches are activated to
apply +Vdc. On the other hand, if current error is positive and smaller than the carrier wave,
the switches are activated to apply –Vdc as Fig 4.
Fig 4: PWM modulation
II.4. Tuning parameters of PI regulator:
With LCL filter, parameters of PI regulators effect significantly on THD of inverter
output current [11].
The conventional tuning methods of PI regulator such as Ziegler-Nichols rules and
GA have been applied to tune the controller recently. Randomly searching technique such as
GA that has high efficient computational and global searching capabilities has been applied
successfully to optimize the complex problems. But the premature convergence of GA
degrades its performance and reduces its searching capabilities. The PSO algorithm is
proposed in this paper to tune PI regulator.
The Ziegler-Nichols method:
Fig 5: Single phase equivalent circuit of LCL filter

297
In Fig 5, when assuming no harmonic at PCC, then Vg=0. For a balanced system the
transfer function of the LCL filter for every phase is given by (11).
;RRC;RRCLLC
;RLCRLCC;LLCC:where
)11(
CsCsCsC
1sRCsLC
)s(V
)s(I
ig4igfig3
gifigf2igf1
43
2
2
3
1
gf
2
gf
i
i
+=++=
+==
+++
++
=
and Ri and Rg are resistors of inductances Li and Lg respectively.
System parameters: Vdc=650V; Ldc=3mH; Rdc=1Ω; Cdc=500µF; grid voltage =380V;
50Hz; short-circuit power=40KVA; Lg=1mH; Rg=0.1Ω; Cf=5µF; Li=2mH; Ri=0.2Ω; carrier
wave frequency fc=9KHz.
Kgh=30 and Tgh=3.888 are determined by Ziegler-Nichols method in (11).
In the GA method with flowchart in Fig 6a
Fig 6a: GA flowchart Fig 6b: PSO flowchart
In the PSO method, velocity and position are updated by equations (12) and (13) in flowchart
in Fig 6b.
)13(V.PP
)12()PP(R.)PP(R.)t(V.wV
curcurcur
curglobes2curlobes1cur
γ+=
−β+−α+=
Results of tuned parameters are shown in table 1
Method Kp_Id Ki_Id Kp_Iq Ki_Iq
Ziegler-
Nichols
13.5 4.182 13.5 4.182
GA 5.6208 200.046 3.4441 1.0156
PSO 4.3523 179.534 2.442 4.0112
Table 1: parameters of PI regulators

298
III. SIMULATION RESULTS AND DISCUSSION
Fig 7: Simulation model in Simulink/Matlab.
The current Id increases from 5A up to 10A at 3.803s.
III.1. Results with Ziegler-Nichols:
Fig 8a: Three-phase voltage (V)
Terminator3
PI_Idq
PI_idq
PI_Vdc
PI_Vdc
0
Iq=0
Idp
[gates]
Goto
[Vdc_ref]
From6
[Vdc]
From5
[Iabc]
From4
[Iabc]
From3
wt
From2
wt
From1
abc
wt
dq0
abc_dq0
Embedded
MATLAB Function1
dq
wt
abc
dq0_abc
Embedded
MATLAB Function
9KHz
I*_abc
Carrier
I_abc
gates
6 xung
wt
wt
650
Vsol
A
B
C
Three-Phase Source
Vabc
A
B
C
a
b
c
Three-Phase
V-I Measurement
Iabc
A
B
C
a
b
c
Three-Phase
I Measurement
a
b
c
A
B
C
Ri_Li
a
b
c
A
B
C
Rg_Lg
Gates
Vso
VDCA
B
C
Inverter
[Iabc]
I
Vdc
Goto3
[gates]
From
a
b
c
A
B
C
C
Vabc (pu)wt
3-phase PLL
3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85
x 10
5
-400
-300
-200
-100
0
100
200
300
400
3-phase voltage (V)

299
Fig 8b: Three-phase current (A)
Fig 8c: Active power P (w) and reactive power Q (var)
Fig 8d: THD spectrum of current
3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85
x 10
5
-10
-5
0
5
10
3-phase current (A)
0 1 2 3 4 5 6 7
x 10
5
-2000
0
2000
4000
6000
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7 3.71 3.72
-4
-2
0
2
4
FFT window: 5 of 288.7 cycles of selected signal
Time (s)
0 200 400 600 800 1000
0
1
2
3
4
Frequency (Hz)
Fundamental (50Hz) = 4.521 , THD= 5.20%
Mag(%ofFundamental)

300
III.2. RESULTS WITH GA:
3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85
x 10
5
-400
-300
-200
-100
0
100
200
300
400
3-phase voltage (V)
3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85
x 10
5
-10
-5
0
5
10
3-phase current (A)
0 1 2 3 4 5 6 7
x 10
5
-2000
0
2000
4000
6000
P (w) & Q (var)

301
III.3. RESULTS WITH PSO:
3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7
-5
0
5
Time (s)
0 200 400 600 800 1000
0
0.5
1
1.5
2
2.5
Frequency (Hz)
Mag(%ofFundamental)
3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85
x 10
5
-400
-300
-200
-100
0
100
200
300
400
3-phase voltage (A)
3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85
x 10
5
-10
-5
0
5
10
3-phase Current (A)

302
thod % THD of output current
Ziegler-Nichols 5.20
GA 3.41
PSO 2.93
Table 2: THD of output current at PCC
IV. DISCUSSION
Parameters of PI regulators in GA and PSO methods always give Kp_Id ≠ Kp_Iq and
Ki_Id ≠ Ki_Iq.
Power responses in figures 8c, 9c and 10c demonstrate that GA and PSO methods
give results better than Ziegler-Nichols method.
The output currents harmonics in figures 8d, 9d and 10d also show that PSO method
in the table 2 gives the best result current THD is 2.93%.
0 1 2 3 4 5 6 7
x 10
5
-2000
0
2000
4000
6000
P (w) & Q (var)
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7 3.71 3.72
-5
0
5
Time (s)
0 200 400 600 800 1000
0
0.5
1
1.5
2
Frequency (Hz)
Mag(%ofFundamental)

303
V. CONCLUSION
This paper presents an approach for a three-phase grid-connected inverter using
current regulator with low current THD by using LCL filter at inverter output and good
response.
The PSO algorithm is proposed in this paper to tune parameters of PI regulator gives
global results better than Ziegler-Nichols and even GA method.
Control strategies proposed is a good alternative to implement an inverter system
control with reduced harmonic content injected into the grid and less computational load than
other methods.
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Three phase grid connected inverter using current

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