A Generalized Parameter Tuning Method of Proportional-Resonant Controllers for Dynamic Voltage Restorers

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 9, No. 4, December 2018, pp. 1709~1717
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v9.i4.pp1709-1717  1709
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
A Generalized Parameter Tuning Method of Proportional-
Resonant Controllers for Dynamic Voltage Restorers
Phuong Vu1
, Ngoc Dinh2
, Nam Hoang3
, Quan Nguyen4
, Dich Nguyen5
, Minh Tran6
1,2,3,5,6
School of Electrical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam
4
Department of Electrical and Computer Engineering, The University of Texas at Austin, Texas, U.S.A
Article Info ABSTRACT
Article history:
Received May 11, 2018
Revised Aug 11, 2018
Accepted Sep 11, 2018
Temporary voltage swells and sags appear with high frequency in electric
power systems, and they significantly affect sensitive loads such as industrial
manufacturing or communication devices. This paper presents a strategy to
design proportional-resonant controllers for three full-bridge voltage-source
converters with a common DC-link in dynamic voltage restorer systems. The
proposed controllers allow the system to quickly overcome temporary
unbalanced voltage sags. Simulation results carried out in
MATLAB/Simulink and experimental results implemented in a Typhoon
HIL402 device demonstrate the ability of the proposed design method. The
results show that the system with the proposed controllers can ride-through
single-phase or double-phase voltage sags up to 55% and three-phase voltage
sags up to 70% in a duration less than one grid-voltage cycle.
Keyword:
Dynamic voltage restorer
Proportional-resonant controller
Hardware-in-the-loop
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Phuong Vu,
School of Electrical Engineering,
Hanoi University of Science and Technology,
No.1, Dai Co Viet Road, Hai Ba Trung, Hanoi, Vietnam.
Email: phuong.vuhoang@hust.edu.vn
1. INTRODUCTION
Power quality disturbances such as voltage sag and swell have been causing serious concerns for
modern distribution systems operated at low- and medium-voltage levels. The percentage of voltage sags
caused by single line-to-ground fault, double line-to-ground fault, and balanced three phase-to-ground fault
in power systems are 68%, 19%, 13%, respectively [1]. Such voltage variations in short durations (less than
60 seconds) lead to improper operation of sensitive loads, while longer voltage variations can result in
sustained interruptions or failures. Therefore, mitigating voltage sags and swells in low- and medium-voltage
distribution systems is critical.
One of the most solution to improve voltage regulation is dynamic voltage restorers (DVRs). The
operating principle of DVRs is to inject appropriate voltage in series and synchronism with the distorted AC
grid source to compensate for the amount of voltage sag or swell [2]-[4]. A DVR system includes an energy
storage, a three-phase voltage-source inverter, and series connected transformers between an AC grid source
and a load. Regarding the three-phase voltage-source inverters, it is necessary to control the positive-,
negative-, and zero-sequence components to compensate the voltage sag or swell of each phase [5].
Therefore, the control scheme is complicated and insufficiently reliable. To eliminate voltage sags and
swells, several alternative topologies of DVR have been introduced such as a three-phase inverters with a
neutral point created by a DC-link capacitor, three-phase four-wire inverters, and three single-phase full-
bridge inverters with a common DC-link capacitor [6],[7]. The latter is preferred because of the simple pulse-
width modulation (PWM) method.
In DVR systems using three full-bridge inverters with a common DC-link capacitor, several control
approaches have been suggested. A coordination of both feed-back and feed-forward control in

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 9, No. 4, December 2018 : 1709 – 1717
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synchronously rotating frame dq is introduced in [8],[9]. However, this topology does not have current loops
to compensate for the losses in the transformers and output filter, which leads to a slow voltage response.
Another approach is to implement proportional-resonant (PR) or Hinf control for the voltage loop and
proportional (P) control for the current loop in the stationary frame αβ [10]. However, controlling only two
components of αβ frame as presented in this approach is not effective when the voltage sag is unbalanced,
which is the typical case in practice. A P control for both voltage and current loops with independent
controllers between each phase is proposed in [11]. This approach is unable to eliminate the steady-state error
in spite of its fast response. A multi-loop with PI controllers is applied to DVR systems in [12], but steady-
state error also exists.
From this literature review, the control strategy using PR controllers for both current and voltage
loops is the most effective for DVR systems to improve dynamic response and eliminate steady-state error
[13]. To the best knowledge of the authors, little research has been done to elaborate on the process of
determining parameters for PR controllers, which is highly complicated. Several studies apply trial and error
procedures to obtain the parameters of PR controllers [14]. Another approach to design PR controllers is
based on the SISO design tool in MATLAB and system dynamic response [15]. Such methods are time-
consuming and not generalized.
This paper proposes a systematic and generalized design method for PR voltage and current
controllers of three single-phase full-bridge inverters with a common DC-link capacitor in DVR systems. The
major contributions of this paper includes:
a) An equivalent circuit of full-bridge inverters and series connected transformers in a DVR system. Unlike
other existing methods, the model of the series transformers is taken into account in this paper when
designing the controllers for the DVR system.
b) A method to design parameters of PR controllers in the frequency domain for both current and voltage
loops to guarantees system stability with a desired cross-over frequency and phase margin. The
discretization in the z-domain of the designed PR controllers for digital implementation is also included.
c) An approach to verify the proposed controller by hardware-in-the-loop (HIL) real-time experiments
using a Typhoon HIL402 device. HIL simulation has been highly recommended as an effective design
approach with the ease in modifying controller parameters and creating different operating scenarios of
grid voltage [16]-[18].
The remainder of this paper is organized as follows. Section 2 describes the general control topology
and the model of a DVR system including the equivalent circuit of full-bridge inverters and series
transformers. The proposed design in the frequency domain of the PR current and voltage controllers is
presented based on the developed equivalent model. The discretization of the designed PR controller is also
included. Section 3 demonstrates the efficacy of the proposed method by off-line simulation and HIL real-
time experiments using Typhoon HIL402 system.
2. CONTROL SCHEME
A scalar control scheme for three full-bridge inverters with a common DC-link capacitor in a DVR
system is shown in Figure 1. Similar controllers are applied separately for each phase corresponding to each
H-bridge inverter. In this control scheme, voltages and currents of all phases are controlled independently
using nested control loops. At each phase, the outer voltage control loop regulates the voltage at the
secondary side of the transformer while the inner current loop regulates the output current of the H-bridge
inverter. The set points of the current loop are the output of the voltage loop, while the set points of the
voltage loop are calculated based on the root-mean-square (RMS) values of the desired voltage (for example,
220 V) and the grid voltage. In the proposed control approach, since the instantaneous voltage and current are
measured, PR controllers are chosen to eliminate the steady-state error. The resonant frequencies of the PR
controllers are equal to the grid frequency. In addition, phase-locked loop (PLL), which is required for grid
synchronization, is implemented by measuring the voltage at each phase of the grid source. In this paper, a
phase-locked loop (PLL) algorithm based on a second-order generalized integrator phase-locked loop (SOGI
PLL) is used [19].
To properly design PR controllers, the model of series transformers in a DVR system should be
taken into account. The equivalent circuit of each H-bridge and the simplified model of the transformer
referred to the secondary side are shown in Figure 2. The leakage impedance of the transformer and
capacitance result in a second-order low-pass filter. The equivalent impedance referred to the secondary side
of the transformer is given as follows:

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
A Generalized Parameter Tuning Method of Proportional-Resonant Controllers for .... (Phuong Vu)
1711
1
2 2
,
p p
eqS s s
r x
Z r j x R j L
N N
s
s s
w
æ ö æ ö
÷ ÷
ç ç
÷ ÷
= + + + = +
ç ç
÷ ÷
ç ç
÷ ÷
ç ç
è ø è ø
(1)
where N is the turns ratio of the transformer, rp and rs are the resistances of the primary and secondary
windings, p
xs and s
xs are the leakage inductances of the primary and secondary windings, and R and Ls are
the resulting resistance and inductance of the equivalent impedance.
Cdc
FB Phase A
FB Phase B
FB Phase C
700 V
S1,2,3,4a
S1,2,3,4b
S1,2,3,4c
Sin
PWM
Udc
Supply
isa
isb
is uc
PR
is
* uabc
is
uc
VAVC_ref
N:1
Voltage controllers Current controllers
+
-
+
-
PR
θ
Sensitive load
PLL
vgrid
Vgrid_RMS
Vref_RMS
220
x
vref
S4
S1
S2
S3
Udc
+
-
-
+
Full bridge
V0_ref_RMS
RMS
isc
vinj
vinj
vinj
vsa
vsb
vsc
C
C
C
Figure 1. Control topology of the inverter in DVR
Xm
rm
Xσp/N2
rs Xσp
vinj C
Grid
Load
S4
S1
S2
S3
Udc
+
-
-
+
vsa/N
Nisa
rp/N2
Figure 2. Equivalent circuit of per phase and series connected transformer
A PR controller has an infinite gain at a selected resonant frequency; thus, the zero steady-state error
or the harmonic at this frequency can be eliminated. The transfer function of a PR controller is
mathematically expressed as follows [20]:
( )
( )
2
2
1
.
c r
PR p
k s
G s k
s w
= +
+
(2)
where p
k and r
k are the coefficients of the PR controller while 1
w is a selected frequency. The frequency
response characteristics of the PR controller are calculated as follows:

 ISSN: 2088-8694
1712
( )
( )
( )
2
2 2 2 2 2
1
2 2
1
p r
PR
k k
G j
w w w
w
w w
- +
=
-
(3)
( )
( )
2 2
0
arctan .
r
PR
p
k
G j
k
w
w
w w
é ù
ê ú
Ð = ê ú
ê ú
-
ë û
(4)
From (3), it can be seen that the PR controller has an infinite gain at 1
w . In [21], the transfer function of the
PR controller with the delay compensation can be written as follows:
( )
( ) ( )
( )
1
2
2
1
cos sin
.
d d
c
PR p r
s
G s k k
s
q w q
w
-
= +
+
(5)
The delay can be compensated by adding a lead angle  
1
d s
kT
 
 to the inverse Park transform
angle, where k is an integer representing the number of periods to be compensated [21]. In this paper, k is set
to 1. To avoid an algebraic loop during the discrete implementation, it is suggested that the direct integrator is
discretized using the forward method while the feedback integrator is discretized using the backward method
[20],[21]. The PR controller with the delay compensation and discrete PR controller is shown in Figure 3.
y
kr
kp
1
s
2
1

1
s
cos(θd)
ω1sin(θd)
x v
u
(a) The PR controller with the delay compensation
x
y
kr
kp
2
1

cos(θd)
ω1sin(θd)
z-1
Delay
1
1
s
T
z
1
1
s
T
z
v
u vpre
(b) The resulting discrete PR controller
Figure 3. Block diagram of PR controllers.
2.1. Design the PR controller for the inner current loop
From Figure 1 and Figure 2, the plant transfer function of current control loop in series converter is
determined as follows:
 
 
  2 2
1
.
1
sa
iv
sa
i s sC
G s
v s N s L C sRC

 
 
(6)
The cross-over frequency is usually selected to be far lower than the sampling frequency fs. On the
other hand, the cross-over frequency fc is significantly higher than the grid frequency f1. From (3),
( ) C
PR pc
G j k
w w
w =
» . The parameter pc
k of the PR regulator for the current loop is thus determined as
follows:
( ) ( )
( )
1
1
.
ci ci
ci
PRc iv
pc
iv
G j G j
k
G j
w w w w
w w
w w
w
= =
=
=
® »
(7)

1713
Next, based on the desired phase margin c
PM of whole system, the parameter rc
k of the PR controller for the
current loop is chosen such that:
( ) ( ) 0
+ 180 .
ci ci
c PRc iv
PM G j G j
w w w w
w w
= =
= Ð Ð + (8)
Therefore, the parameter rc
k of the PR regulator is determined as follows:
( )
2 2
1
arctan r ci
c
p ci
k
A
k
w
w w
é ù
ê ú
=
ê ú
ê ú
-
ë û
(8)
( ) ( )
2 2
0
tan
,
c p ci
rc
ci
A k
k
w w
w
-
® = (10)
where ( ) 0
- 180
C
c c iv
A PM G j w w
w =
é ù
= +
ê ú
ë û
.
2.2. Design the PR controller for the outer voltage loop
From Figure 2, the plant transfer function of voltage control loop in series converter is determined as
follows:
 
 
 
1
.
inj
vi
c
v s
G s
i s Cs
  (11)
The magnitude-frequency and phase-frequency response of  
vi
G s can be written as follows:
    0
1
, 90
vi vi
G j G j
C
 

    (12)
( ) ( ) 1
.
cv cv
PRv iv
pv cv
G j G j
k C
w w w w
w w
w
= =
=
® »
(13)
From the desired phase margin v
PM of whole system, the parameter rv
k of the PR controller is chosen such
that:
( ) ( ) 0
+ 180 .
cv cv
v PRv vi
PM G j G j
w w w w
w w
= =
= Ð Ð + (14)
Therefore, the parameter rv
k of the PR regulator is determined as follows:
( )
2 2
1
arctan rv cv
v
pv cv
k
A
k
w
w w
é ù
ê ú
=
ê ú
ê ú
-
ë û
(15)
( ) ( )
2 2
0
tan
,
v p cv
rv
cv
A k
k
w w
w
-
® = (16)
where
0
-90
v v
A PM
= .

 ISSN: 2088-8694
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3. RESULTS AND ANALYSIS
3.1. Simulation results
The proposed control topology is validated using MATLAB/Simulink/Simpower Systems. The DC
voltage is 700VDC while the transformer turns ratio N is 2. The total of leakage inductance Ls in (1) is
0.2975mH, the filter capacitance C is 30µF, and the switching frequency fs is 5kHz. Unipolar PWM
technique is implemented to control the switching of the IGBT switches of the H-bridge inverters [19]. The
phase margin and cross-over frequency of current loop are chosen to be 450
and 500Hz, respectively. The
phase margin and cross-over frequency of voltage loop are chosen to be 450
, and 200Hz, respectively.
This paper investigates the following transient scenarios of the grid voltage: single-phase 55%
voltage sag (0.1-0.2s), double-phase 55% voltage sag (0.25-0.35s), and three-phase 70% voltage sag (0.4-
0.5s). The RMS value of the phase-to-phase grid voltage is 380 VAC, i.e. the phase-to-neutral voltage is
220VAC. The three-phase voltage sags are created by a programmable voltage source in Matlab/Simpowwer
Systems.
Figure 4 and Figure 5 show the response of the DVR system with the proposed control during the
supply voltage sags. It is clear that the DVR is able to restore correctly to the nominal value within just one
cycle of grid voltage (20 ms). The overshoots of the load voltage are negligible, and the steady-state error of
injected voltage and inverter current is eliminated in the three cases in Figure 5. A dramatic part of the delay
is due to the calculation of the root mean square (RMS) of supply voltage.
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-400
-200
0
200
400
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-200
-100
0
100
200
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-400
-200
0
200
400
Supply
voltage
(V)
Injected
voltage
(V)
Load
voltage
(V)
Time(s)
Figure 4. Measured response of DVR (grid voltages,
voltages injected by the DVR, load voltages)
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-150
-100
-50
0
50
100
150
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-200
-100
0
100
200
Injected
voltage_phase
a
(V)
Inverter
current_phase
a
(A)
Ref
Act
Ref-Act
Ref-Act
Time (s)
Figure 5. The reference and actual voltage and
current of phase a
3.2. Hardware-in-the-loop experimental results
The proposed control is also verified in HIL environment using a Typhoon device. This device
consists of an HIL402 card that simulates grid source, load, and three full-bridge with a common DC-link
capacitor using IGBTs. The hardware system is simulated in real time on the HIL platform with a time step
of 1 μs, which is close to the physical model. The carrier frequency of the PWM is 5 kHz. The voltage and
current controllers as well as PLL are implemented in the DSP TMS320F2808 card.
All data of HIL is recorded by the Typhoon HIL Control Center Software and shown in Figure 6.
The load voltage and the injected voltage from the DVR system are measured using the oscilloscope
HAMEG –200MHz at test points in the HIL DSP interface of Typhoon. These voltages are shown in Figure
7. It is clear that the responses of the HIL experimental results are similar to those in the simulation results in
MATLAB. The DVR system is able to regulate the load voltage with an ignorable overshoot within an
acceptable period (less than 20 ms) in the injection mode. When supply voltage stable at the nominal value,
the DVR system is operated in the standby mode, which means no voltage is injected.

1715
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
-200
-100
0
100
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-500
0
500
Supply
voltage
(V)
Injected
Voltage
(V)
Load
Voltage
(V)
Time (s)
Figure 6. HIL experimental results: supply voltage, injected voltage, and load voltage
Load voltages
Voltages injected by the DVR.
Load voltages
Load voltages
a. Single-phase 55% voltage sag b. Double-phase 55% voltage sag c. Three-phase 70% voltage sag.
Figure 7. HIL experimental results in different operating conditions
4. CONCLUSION
This paper proposes a systematic and generalized design method for PR controllers of three single-
phase full-bridge inverters with a common DC-link capacitor in DVR systems. The proposed control is
designed for each single-phase inverter, taken into account the model of the series transformers. MATLAB
and the HIL experimental results validate the performance of voltage in scenarios: single-phase and double
phase voltage sags up to 55%, and three-phase voltage sag up to 70% within acceptable periods. The results
prove that the DVR system is able to protect the load from voltage sags due to these various types of faults.
Such promising results create a crucial foundation for the application of DVR systems in industry.
ACKNOWLEDGEMENTS
This research was funded by the Ministry of Science and Technology (Vietnam) under project
number KC.05.03/16-20.

 ISSN: 2088-8694
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BIOGRAPHIES OF AUTHORS
Phuong Vu received his B.S., M.S., and Ph.D. degrees from Hanoi University of Science and
Technology, Vietnam, in 2006, 2008, and 2014, respectively, all in Control Engineering and
Automation. Since 2006 he has been employed at Hanoi University of Science and Technology,
where he is a lecturer and researcher at school of electrical engineering. His research interests
include modeling and controlling of power electronics converters for applications such as
photovoltaic, wind system, electrical machine drive.

1717
Ngoc Dinh was born 1994. He received his Engineer’s degree from Hanoi University of Science
and Technology, Vietnam in 2017, in Electrical Engineering. He is currently pursuing M.Sc at
Hanoi University of Science and Technology and working Institute for Control Engineering and
Automation - ICEA. He research interests are power electronics on the DSP and FPGA platform.
Nam Hoang was born 1994. He received his Engineer’s degree from Hanoi University of Science
and Technology, Vietnam in 2017, in Electrical Engineering. He is currently pursuing M.Sc at
Hanoi University of Science and Technology. He research interests are multilevel converter and
power electronics.
Quan Nguyen received his Bachelor’s degree from Hanoi University of Science and Technology,
Vietnam in 2012 and the M.S degree from The University of Texas at Austin, USA in 2016, both
in Electrical Engineering. He is currently pursuing a PhD at The University of Texas at Austin. His
research interests are power system control and optimization, renewable energy integration, power
quality, and power electronics.
Dich Nguyen received the B.S. degree in electrical engineering from Hanoi University of
Technology, Hanoi, Vietnam, in 1997. He received the M.S. degree in electrical engineering from
the Dresden University of Technology, Dresden, Germany and Ph.D from Ritsumeikan University,
Kusatsu, Japan, in 2003 and 2010, respectively. Since 2000, he has been with Hanoi University of
Science and Technology, Vietnam, where he is currently an Associate Professor and Executive
Dean of the Institute for Control Engineering and Automation. His research interests include
magnetic bearings, selfbearing motor, and sensorless motor control.
Minh Tran received his B.S. degree Technical university in Bacu, in 1983. He received his M.S.
degree from Asian Institute of Technology, Thailand and Ph.D from Hanoi University of Science
and Technology, Vietnam, in 2007 and 2014, respectively. Since1983, he has been with Hanoi
University of Science and Technology, Vietnam, where he is currently an Associate Professor and
Executive Dean of the Department of Industrial Automation. His research interests include
modelling and controlling of power converters, multilevel converter, HVDC transmission
technology.

A Generalized Parameter Tuning Method of Proportional-Resonant Controllers for Dynamic Voltage Restorers

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A Generalized Parameter Tuning Method of Proportional-Resonant Controllers for Dynamic Voltage Restorers