Phuong Vu, Nam Hoang, Ngoc Nguyen, Quan Nguyen, Minh Tran;”A systematic parameter tuning of PI current controller for LCL-type active rectifiers under unbalanced grid voltage conditions”; Journal of Electrical Systems.

1. *
Corresponding author: Phuong Vu, PhD, School of Electrical Engineering, Hanoi University of Science and
Technology, Hanoi, Vietnam
1
School of Electrical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam
2
Department of Electrical and Computer Engineering, The University of Texas at Austin, Texas, USA
3
Hanoi University of Industry
E-mail: phuong.vuhoang@hust.edu.vn
Copyright © JES 2010 on-line : journal/esrgroups.org/jes 48
Phuong Vu1,*
,
Nam Hoang1
Ngoc Nguyen1
Quan Nguyen2
,
Minh Tran1
,
Hung Do3
J. Electrical Systems x-x (xxxx): xxx-xxx
Regular paper
A systematic parameter tuning of PI
current controller for LCL-type active
rectifiers under unbalanced grid voltage
conditions
Active rectifiers are widely employed in three-phase electric drive or renewable energy resource
systems because of the bidirectional power flow and the power factor correction. This paper proposes a
systematic method to determine the parameters for the PI current controllers in active rectifier systems
using LCL filter under unbalanced grid faults. The parameters of PI regulators are designed in frequency
domain and taking into account the full model of the LCL filter as well as the time delay in control
system, which improves the system stability and reliability. The simulation results in MATLAB and
hardware-in-the-loop experimental simulation using the HIL 402 device of Typhoon validate the robust
and capability of active rectifier in stabilizing the system under different non-ideal conditions of grid
voltage.
Keywords: Active filters, current controllers, LCL filters, unbalanced grid voltage.
1. Introduction
Active rectifiers based on three-phase inverters, with LCL filters and with/without
isolation transformers, have been using widely in various electrical systems [1]. The
advantages of active rectifiers include bidirectional power flow between AC grids and
loads, controllable power factor, low harmonic content (less than 5% according to IEEE519
standard) in the waveform of the current injected into AC grid. In three-phase electric drive
systems, active rectifiers allow high DC voltages for fast dynamic responses or a common
DC source for the energy saving purpose in multi-machine systems [2]. Active rectifiers are
also the interface that allows bidirectional power delivery between AC grids and renewable
energy resources such as wind and solar [3][4]. Other important applications of active
rectifiers include active filters and active voltage conditioner [5][6].
In spite of their prevalent applications, the control topology of active rectifiers is highly
complicated, and it requires both positive- and negative-sequence control under unbalanced
grid voltage conditions [7], [8]. In addition, with the use of the LCL filter, the control
topology must take into account additional devices that damp out the passive and active
oscillations [9], [10]. To damp out active oscillations, it is necessary to increase the number
of sensors to measure the grid and capacitor currents, which leads to a high overall cost and
complex control strategies. Therefore, passive damping is preferred in industry by
connecting resistors with capacitors in LCL filters to improve reliability.
In an active rectifier system based on a three-phase inverter, the output inverter current
must be measured and controlled to protect the switching devices. The parameters of the
current controller is designed based on the transfer function of the inverter voltage to the
inverter current. Previous works usually simplify the model LCL filters as L filters to easily
determine these parameters of the PI [11]-[13]. However, the resulting first-order transfer
function of the inverter voltage to the inverter current does not reflect exactly the third-

2. J. Electrical Systems 6-4 (2010): 466-479
49
order transfer function when LCL filters are employed. In some studies, many trial and
error procedures have been carried out to obtain a set of parameter of PI regulators [7]. This
simplification reduces the quality of the current loop in terms of the transient time,
overshoot, or system stability.
The contribution of this paper is to propose a systematic parameter tuning of PI current
controllers for the LCL-type active rectifier under unbalanced grid voltage conditions. The
parameters of the current controllers are designed in the frequency domain taking into
account the full model of LCL filters and time delay in control system based on desired
phase margin and crossover frequency to guarantee the stability of the whole control
system. The proposed approach enhances the capability of active rectifiers in regulating the
DC voltage under unbalanced conditions of grid voltage such as up to 70% three-phase
voltage sags and up to 55% double-phase or single-phase voltage sags. Simulation results in
MATLAB and experimental results using the hardware-in-the-loop (HIL) 402 device of
Typhoon verify the capability of the proposed current-controller design method in such
fluctuating conditions of grid voltage.
2. Notation
The notation used throughout the paper is stated below.
Indexes:
PLL Phase locked loop
PM Phase margin
THD Total Harmonic Distortion
DSRF Double synchronous reference frames
Constants:
 sviG s The transfer function from inverter-side voltage to inverter-side current
 gviG s The transfer function from inverter-side voltage to grid-side current
 PIG s The transfer function of PI controller in s domain
1 fundamental frequency of grid voltage
3. A systematic method to determine the parameters for the PI current controllers
The control topology of active filters is implemented in a double synchronous reference
frames (DSRF), as shown in Fig. 1. It contains of AC current and DC voltage control loops.
The AC current loop controls both the positive- and negative- sequence components, which
are given from two synchronous reference frames rotating at the fundamental grid
frequency in the positive and the negative directions respectively. The positive- and
negative- sequence components as well as the phase angle of grid voltage are calculated by
the decoupled double synchronous reference frame PLL (DDSRF-PLL). DDSRF-PLL is an
effective synchronization solution for three phase power converter under unbalanced grid
faults [13]. The pulse width modulation method employed in this control topology is the
space vector modulation. The outer DC-voltage control loop regulates the voltage across
the DC-link capacitor, and it is used to calculate the reference value for the inner AC
current loop.
The current vector in both synchronous reference frames is given as follows:
1 1
1 1
cos(2 ) sin(2 )cos
cos( ) sin( )
sin(2 ) cos(2 )sin
d dd
dq
q qq
ACtermsDCterms
t ti i i
i I I I
t ti ii
(1)

3. Phuong Vu et al: A novel current controller design for active rectifiers using LCL filters under
unbalanced grid voltage conditions
50
1 1
1 1
cos(2 ) sin(2 )cos
cos( ) sin( )
sin(2 ) cos(2 )sin
d dd
dq
q qq
ACtermsDCterms
t ti i i
i I I I
t ti ii
(2)
The effect of the 12 oscillation in (1) and (2), which resulting from the cross-coupling
between the reference frames and current vectors with different sequences, is cancelled by a
first-order low pass filter (F). The cut-off frequency of the F is set to 1 2fc [13].
Therefore, the strategy would work properly provided that the PI controller are able to track
the DC references perfectly [13].
PLL
ωL
ωL
ωL
ωL
-
SVM
C
Vdc
Va
Vb
Vc
Vdc*
LPF
abc
αβ
αβ
αβ
dq-
dq+
abc
αβ
[F]
[F]
+
+
+
+
+
-
-
-
--
+
-+
+-
-+
+-
-
-+
+
++
Ia
Ib
Ic
Li
Lg
Cf
+-
αβ
dq+
αβ
dq-
αβ
dq+
dq-
αβ
vαβ
Vαβ
Sabc
iαβ
G1 G4
G3 G6
G5 G2
LPF
LPF
LPF
Pos. seq. current controller
DC voltage controller
P0Idc*
Neg. seq. current controller
rd
Equation (12)
en
Fig. 1. The control topology of an active rectifier in an unbalanced voltage grid.
With the LCL filter, the transfer function between the output voltage and current of the
active rectifier is determined as follows [13]:
2 2 2
2 2 2
1
s
d f LC LCs
vi
s i d f res res
s r C z s zi s
G s
v s L s s r C s
(3)
 
 
   2 2 2
0
11
g
n
g d f
vi
s d f res rese
i s r C s
G s
v s Ls s r C s 

 
 
(4)

4. J. Electrical Systems 6-4 (2010): 466-479
51
where
12
LC g fz L C and 2 2
res g i LC iL L z L . The responses in the frequency domain
of sviG s and  gviG s with the LCL-filter are shown in Fig. 2. It is clear that there is a
third-order filter with an attenuation of 60dB/decade above the resonant frequency. Thus,
LCL filters can be used for converters with low switching frequency.
-120
-100
-80
-60
-40
-20
0
Magnitude(dB)
10
2
10
3
10
4
10
5
-225
-180
-135
-90
-45
0
Phase(deg)
Bode Diagram
Frequency (Hz)
Gvis
Gvis
Gvig
Gvig
Fig. 2. Responses in the frequency domain of sviG s and  gviG s .
The parameters of the PI controller is calculated by a simplified current loop in Fig.3 and
neglecting the coupled d- and q- current components. The computation delay and the
behavior of the pulse-width modulation module are represented by 1.5Ts, where Ts is the
sampling time [14].
*
si siic
pc
K
K
s
1
1.5 13
ce
s
v
T s
m
viG s
PIG s pwmG s
vs
Fig. 3. A simplified current loop for active rectifier.
With the transfer function shown in (3), the parameters of the PI controller for the
current loop are calculated in the frequency domain as follows. First, the cross-over
frequency fc is chosen as shown in (5), where fs and fres are the sampling frequency and the
resonant frequency of the LCL filter. The cross-over frequency is usually selected to be far
lower than the sampling frequency fs and much smaller than the resonant frequency fres
[15].
10
4 2
s
c
s s
res
f
f
f f
f



  

(5)
The magnitude of the PI controller is given as follows:
2
2
2
ic
PI pc
K
G j K (6)

5. Phuong Vu et al: A novel current controller design for active rectifiers using LCL filters under
unbalanced grid voltage conditions
52
Since the cross-over frequency is significantly higher than the grid frequency,
C
PI pcG j K . The parameter pcK of the PI regulators for the current loop is thus
determined as follows:
w
w
1
1
C CC
C C
PI p m vi
pc
vi p m
G j G j G j
K
G j G j
(7)
Next, based on the desired phase margin PM*
of whole system, the parameter icK of the PI
controller is chosen such that:
0
+ + 180
C CC
PI pwm viPM G j G j G j (8)
Therefore, the parameter Kic of the PI regulators is determined as follows:
2
1
arctan
tan
ic
pc c
ic pc c
K
A
K
K A K
(9)
where:
* 0
PM - + 180
C C
vi pwmA G j G j (10)
Equation Error! Reference source not found. defines how the positive-sequence grid
current controllers achieve everage values of the instantaneous active power P0 and reactive
power Q0 requirements.
1
*
0
*
0
*
2
* 2
2
3
gd nd nq nd nq
gq nq nq nq nd
cgd nd nq nd nq
s
gq nq nd nq nd
i e e e e P
i e e e e Q
Pi e e e e
Pi e e e e
(11)
For the active rectifier, P0 is the output of DC voltage controller, and Q0 is set to zero. To
support power quality requirements, the double-frequency oscillating power components
Pc2 and Ps2 are set to zero, which means zero * *
,gd gqi i references, so that the currents towards
the grid are sinusoidal [7], [13]. In steady state, the inverter current is the same as the grid
current if the power loss in rdC filter is neglected.
4. Simulation results
The control topology at the grid side is simulated in MATLAB/Simulink/Simpower
Systems. The simulation parameters of the test system are shown in Table I.
Table 1: Simulation parameters
Rated power 5 kVA
Grid voltage 380 VAC / 50 Hz
Equilibrium DC voltage (vce) 700 V
Switching frequency 5 kHz
DC capacitance 1650 µF

6. J. Electrical Systems 6-4 (2010): 466-479
53
LCL filter
Grid and Converter side
inductance
Lg = 1.2 mH,
Li = 3.5 mH
Filter capacitance 6.8 µF
Damping resistor 4 Ω
Parameters of current controller
Kpc 0.0513
Kic 5.0995
With the filter parameters shown in Table I, the phase margin PM*
and the cross-over
frequency are chosen to be 450
and 500 Hz, respectively. The parameters of the PI
controller are calculated using the method described in Section 3 and shown in Table I. The
Bode diagram that represents the characteristics of the current control loop with the
implementation of the designed PI controller are shown in Fig. 4. The current loop is shown
to be stable and the phase margin is exactly 450
at 500 Hz.
-100
-50
0
50
100
Magnitude(dB)
10
0
10
1
10
2
10
3
10
4
10
5
-180
-150
-120
-90
Phase(deg)
Bode Diagram
Frequency (Hz)
Phase Margin (deg): 45
Delay Margin (sec): 0.00025
At frequency (Hz): 500
Closed loop stable? Yes
Fig. 4. Responses in the frequency domain of open current loop.
With the design PI controllers, this paper investigates the following scenarios of an
unbalanced grid: single-phase 55% voltage sag at 0.3s, double-phase 55% voltage sag at
0.45s, three-phase 70% voltage sag 0.6s, three-phase 110% voltage swell 0.75s, total
simulation time is 0.85s.
The simulation results are shown in Fig.5 and Fig.6. During the starting process of an
active rectifier, three resistors connected in series with the inverter at the AC side to charge
the DC capacitor to avoid current strikes. When the capacitor voltage is higher than 400 V,
these resistors are by-passed, and the capacitor voltage is 540 V. When the control signal is
sent to the inverter at 0.15s, the capacitor voltage follows the set point of 700 V after 0.05
second. When a fault occurs, the capacitor voltage stabilizes quickly in all four conditions

7. Phuong Vu et al: A novel current controller design for active rectifiers using LCL filters under
unbalanced grid voltage conditions
54
with fast transient times and low overshoots. Grid voltage and current are in phase with
each other, resulting in unit power factor. In steady state and balanced supply voltage, the
total harmonic distortion (THD) of grid current measured by the FFT Tool in Matlab is
2.54%.
The negative-sequence current components are enforced to zero at the instant of
unbalanced voltage conditions, and deteriorated grid current waveforms are dissipated.
Because of reactive power Q0 is set to zero, the *
gqi is tracked to zero. It is clear that
gdi completely tracks the references in steady-state condition without any overshoot.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
500
1000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-500
0
500
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-50
0
50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-50
0
50
Vdc(V)vgrid(V)igrid(A)idq(A)
0.4 0.41 0.42 0.43
695
700
705
0.25 0.26 0.27 0.28
-20
0
20
Fig. 5. MATLAB simulation results: grid voltage, grid current, and DC voltage in
different working conditions.

8. J. Electrical Systems 6-4 (2010): 466-479
55
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-50
0
50
id+(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-20
0
20
iq+(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-50
0
50
id-(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-50
0
50
iq-(A)
Fig. 6. The positive- and negative- sequence of the dq-axis currents.
5. Hardware-in-the-loop experimental results
To verify the proposed control and conveniently simulate the aforementioned
unbalanced operating conditions of grid voltage, this paper uses the standard Typhoon HIL
device shown in Fig. 7 [16]-[18]. This device consists of an HIL 402 card that simulates a
grid source, an LCL filter, and a three-phase voltage source inverter using IGBTs. The
system hardware is simulated in real time using the HIL platform with a time step of 1 μs,
which closely represent the real physical model. The pulse width modulation (PWM)
carrier frequency is 5 kHz. The DC-voltage and current controllers as well as the PLL
algorithm are implemented in DSP TMS320F2808 card.
Fig. 7. The hardware setup for the HIL platform.

9. Phuong Vu et al: A novel current controller design for active rectifiers using LCL filters under
unbalanced grid voltage conditions
56
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-400
-200
0
200
400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-40
-20
0
20
40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
200
400
600
800
0.28 0.31 0.34
690
700
0.53 0.55 0.57
700
720
0.68 0.7 0.72 0.74
705
715
725
Supplyvoltage(V)Gridcurrent(A)DCvoltage(V)
Time (s)
Fig. 8. HIL experimental results: Grid voltage, grid current, and DC voltage in different
working conditions.
All data of HIL is recorded by Typhoon HIL Control Center Software and illustrated in
Fig.8. In all four scenarios, the transient times of the DC voltage have low overshoot, and
this DC voltage remains stable at 700VDC. The responses of the HIL experimental results
are consistent with those shown in Section III.
6. Conclusion
This paper proposes a novel control topology and a design method of current controllers
for three-phase active rectifiers under non-ideal grid conditions considering the third-order
model of LCL filters. MATLAB and the HIL experimental results show very good dynamic
responses of the DC voltage and AC output current in four working conditions: single-
phase and double phase voltage sags up to 55%, three-phase voltage sag up to 70%, and
three-phase voltage swell up to 110%. These promising results creates a crucial foundation
to extend the applications of active rectifiers in dynamic voltage restorers, active filters, and
power electronics interfaces between renewable energy resources and AC grids.
Acknowledgment
This research is funded by Hanoi University of Science and Technology (HUST) under
project number T2017-PC-109.
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