Modelling of a Two-Stage Bidirectional AC-DC Converter using Wavelet Modulation

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 9, No. 3, September 2018, pp. 1006~1015
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v9.i3.pp1006-1015  1006
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Modelling of a Two-Stage Bidirectional AC-DC Converter using
Wavelet Modulation
H.K. Chiu1
, Agileswari K. Ramasamy2
, Nadia M.L. Tan3
, Matthew Y.W. Teow4
1,3
Department of Electrical Power Engineering, Universiti Tenaga Nasional, Malaysia
2
Department of Electronics and Communication Engineering, Universiti Tenaga Nasional, Malaysia
4
Faculty of Engineering and Computing, First City University College, Malaysia
Article Info ABSTRACT
Article history:
Received May 3, 2018
Revised Jul 20, 2018
Accepted Jul 28, 2018
In this paper, a Wavelet modulated isolated two-stage three-phase
bidirectional AC-DC converter is proposed for electric vehicle (EV) charging
systems. Half-bridge resonant CLLC converter is proposed due to its high
efficiency, wide gain range, galvanic isolation and bidirectional power flow.
Wavelet modulation technique is used for three-phase six leg AC-DC
converter due to its benefits of high DC component and lower harmonic
contents. The proposed two-stage converter is developed and simulated in
MATLAB Simulink environment. The contribution of this paper is on the
implementation and performance analysis of Wavelet modulation in
bidirectional AC-DC converters. The results show that Wavelet modulation
is suitable to be implemented for the proposed bidirectional converter. The
performance of the proposed converter delivers very low output voltage
ripple and total harmonic distortion output current of less than 10% which is
within the expected results.
Keyword:
Bidirectional AC-DC converter
Half-bridge CLLC resonant
Converter
Resonant converter
Wavelet modulation
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
H.K. Chiu,
Department of Electrical Power Engineering,
Universiti Tenaga Nasional,
Jalan Ikram-Uniten, 43000 Kajang, Selangor Darul Ehsan, Malaysia
Email: PE20689@utn.edu.my
1. INTRODUCTION
Electric vehicle (EV) has gained much attention in the last decade as a promising solution to
greenhouse gas (GHG) emissions in the transportation sector. One of its main advantages is to reduce
dependency on fossil fuels as a source of fuel supply for vehicles. EVs also have the benefits of providing
additional support to the electric power grid such as ancillary services and load balancing [1]. For EVs to
compete with conventional combustion engine performance, high efficiency of EV chargers are required to
deliver optimum performance and energy saving for the consumers. There are many different converter
topologies and systems proposed for single-stage and two-stage topologies [1]-[8]. Two-stage topologies
have the disadvantage of increased cost and size due to having two stages of energy conversion however, this
has the advantage of having a fixed DC link voltage, simplifying the DC-DC converter [1]-[2].
Wavelet modulation is a modulation strategy that is currently used in inverters and multilevel
inverters [10]-[14]. The advantages of wavelet modulation compared to existing modulation techniques is
that it does not require a carrier signal, generates a higher magnitude of the fundamental component in the
output voltage and lower harmonic distortion compared to other pulse width modulation (PWM) methods
such as sinusoidal PWM (SPWM), space vector PWM (SVPWM), phase shifted PWM (PSPWM) and level
shifted PWM (LSPWM) [13],[15]. Therefore, the contribution of this paper is on the implementation and
performance analysis of Wavelet modulation in bidirectional AC-DC converters and also a new two-stage
topology that can be implemented for bidirectional EV chargers.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Modelling of a Two-Stage Bidirectional AC-DC Converter using Wavelet Modulation (H.K. Chiu)
1007
In this paper, a two-stage bidirectional AC-DC converter is proposed, using six switch AC-DC
converter and half-bridge CLLC resonant converter. Previous studies have shown that half bridge CLLC
resonant converters are able to provide high power density, high efficiency, and the additional capacitors in
each leg allows reduction of flux imbalance for the transformer [3]-[6]. The proposed converter has two
converters, the bidirectional AC-DC converter connected to a three-phase grid and DC voltage link
controlled using Wavelet modulation and a half-bridge CLLC resonant converter controlled using frequency
modulation. The following chapters of this paper would elaborate on the wavelet modulation strategy used,
design considerations for the proposed two-stage bidirectional converter, the simulated results obtain using
MATLAB Simulink, conclusion and the potential areas to improve this converter.
2. WAVELET MODULATION CONTROL
The wavelet modulation technique for inverters has been implemented using sampling theorem and
nondyadic-type multiresolution analysis (MRA) [11]-[15]. The signals required to operate a power electronic
converter is modeled and optimized using sets of newly developed scale-based linearly combined scaling and
synthesis wavelet basis functions. In order to realize wavelet modulation technique which requires the
nondyadic MRA to sample and reconstruct the reference signal, the analysis stage and synthesis stage is
required as shown below:
Analysis Stage :The referenced signal (desired output signal) is sampled using scale-based linearly
combined scaling basis, {𝜑(2𝑗
𝑡 − 𝑘}𝑗,𝑘∈ℤ which develops groups of nonuniform recurrent
samples that is vital in determining the width and location of one ‘ON’ state pulse
Synthesis
Stage
: The reference signal is now reconstructed from the groups of samples obtained in
theanalysis stage. These synthesized functions are used as ON switching states for the
power electronic converter.
The three sets of groups of nonuniform recurrent samples from reference signal are as follows [12]:
(1)
(2)
(3)
where j1 = 1,2. . . , J, j1 ∈ ℤ, j2 = j1 + J − 3, j2 ∈ ℤ, j3 = j1 + J − 2, j3 ∈ ℤ and J is the
maximum value of j.
The reconstruction of reference signal is accomplished with three synthesis basis functions which
are generated by the shifted versions of Equation 1 to 3. The three synthesis scaling functions are defined as
follow [12]:
(4)
(5)
(6)
where 𝜙𝐻(𝑡) is the Haar scaling function [13] and 𝜑
̃(𝑡) is the scale-based linearly combined
function. The nondyadic type MRA representation of three continuous time (CT) reference modulating
signals for the output voltage of each phase (inverter) with respect to the DC voltage is shown below [13]:
(7)

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 9, No. 3, September 2018 : 1006 – 1015
1008
(8)
(9)
where Tm is the period of the sinusoidal function, v(t) is the output voltage per phase and VDC is the
input voltage. For the output voltage at DC link (Rectifier), it can be derived as shown below [12]:
(10)
The inner biproduct operation is derived as below for Equation 10 for one of the phases:
(11)
(12)
where Tm is the period of the AC input and Sdc(t) is the reference DC voltage with respect to time. Lastly, the
samples in each group (each phases) da, db and dc are located at the boundaries of [tda1,tda2], [tdb1,tdb2] and
[tdc1,tdc2]. The time locations are obtained to determine switching intervals for each of the phase leg. The time
locations are determined as follow [14]:
(13)
(14)
(15)

1009
The key differences between modulating for rectifier operation and inverter operation are the
reference signal required and how the set of groups of samples are computed based on the number of
reference signals. Another notable difference is the scales j1, j2 and j3. During rectifier mode, the changes
are based on the input AC voltages while during inverter mode, it is changed based on the reference signal.
3. DESIGN CONSIDERATIONS FOR THE PROPOSED CONVERTER
In this paper, a two-stage bidirectional AC-DC converter is proposed, using six switch AC-DC
converter and half-bridge CLLC resonant converter.The proposed converter has two converters as shown in
Figure 1, where the bidirectional AC-DC converter is connected to a three-phase grid and is controlled using
Wavelet modulation and a half-bridge CLLC resonant converter controlled using frequency modulation.
Figure 1. Proposed two-stage bidirectional AC-DC converter
The bidirectional half-bridge CLLC converter has two power flow modes: charging (power flowing
from DC link voltage to the battery) and discharging (power flowing from the battery to the DC link voltage).
The equivalent circuit of the half-bridge CLLC resonant converter is shown in Figure 2 for both modes. Re,
L’2, C’21 and C’22 are the equivalent to Ro, L2, C21 and C22 of the converter respectively.
(a) (b)
Figure 2. Equivalent circuits of half-bridge CLLC converter in
(a) charging mode and (b) discharging mode [9]
A detailed derivation for Re for full-bridge CLLC converter can be obtained in [4] by using First
Harmonic Approximation (FHA) method. For the half-bridge CLLC converter in charging mode, the
parameters can be expressed as [9]:
(16)
While the parameters during discharging mode can be calculated as [9]:

 ISSN: 2088-8694
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(17)
Given that the L and C will be of same values in both modes, the resonant frequency for both the
modes will be identical.
4. RESULTS AND ANALYSIS
The previous sections presented the methodology to develop the time boundaries for each of the
phase leg of the bidirectional AC-DC converter and the design considerations to determine the component
values of the half bridge CLLC converter based on its equivalent circuit. The bidirectional three-phase six
pulse AC-DC converter is modulated using Wavelet modulation technique while the half-bridge CLLC
converter is controlled using frequency modulation. Simulation results were obtained using MATLAB
Simulink for the rated output power of 1 kW, as shown in Figure 3. In the blue area as highlighted in Figure
3, shows the six-switch three-phase bidirectional AC-DC converter and the Wavelet modulation block while
the red area shows the half-bridge CLLC resonant converter and its frequency modulation block.
The main objective of this simulation is to investigate the features of the inputs and outputs of the
proposed converter during charging and discharging mode. The design parameters and components used for
the simulation is shown in Table 1. The input three phase voltage for this converter would be 415 VAC at 50
Hz, the DC link voltage is adjusted to be 500 V and the output of the CLLC resonant converter is set at 250
V. The switching frequency for the half-bridge resonant CLLC converter is set at 230 kHz. The sampling
time, Ts for the simulation is set at 50 µs. The power electronic switches used for the bidirectional AC-DC
converter are ideal IGBTs in simulation and MOSFETs with with internal diode in parallel with RC snubber
circuit for the bidirectional DC-DC converter. The developed SIMULINK model of the proposed converter is
tested on a load of 176 Ω (RO) [9]. The results obtained from the simulation will be displayed and discussed
in this section.
Figure 3. Simulation model of the proposed converter in Simulink
Figure 3. Simulation Model of the Proposed Converter in Simulink
Components Values
RL Filter 1 Ω and 10 mH
DC Link Capacitor 4700 µF
C11 and C12 14.2 nF
L1 32 µH
L2 15 µH
C21 and C22 33 nF
RO and C6 176 Ω and 1000 µF

1011
Transformer
Turn ratio
Lm
1.5
120 µH
Figure 4 shows the DC link voltage output of the converter during rectifier mode. The average
output DC was obtained around 520 V. The reason why the DC voltage is higher than the expected rating of
500 V is due to the Wavelet modulation not having any feedback to control the output voltage. Figure 5
shows the DC link voltage during inverter mode at 500 V. The output DC link voltage was obtained through
the bidirectional CLLC resonant converter. Although there are some ripple observed in the results obtained,
the root mean square (RMS) value of the voltage is still within acceptable results.
Figure 6 and 7 shows the input AC current of the proposed bidirectional AC-DC converter. The total
harmonic distortion of the current (THDi) was computed in Simulink which is obtained by diving the RMS
value of the total harmonics of the signal by the RMS value of its fundamental signal. The THDi obtained
during rectifier mode is 7.2% while the THDi during inverter mode is 6.2%. The THD results can be further
reduced if optimization techniques to control the phase and current was included with the Wavelet
modulation scheme at the cost of increased complexity in the control structure.
Figure 8 shows the line-to-line voltage VL-L at the three-phase supply during inverter/discharging
mode. The RMS value of the VL-L was measured at 390 V. The THDV obtained for this voltage is 47% which
is slightly high for the current technology of inverters. One of the few ways to improve the harmonics of the
result is by changing the scale J to a larger value and to include filters before connecting to the grid. Figure 9
shows the output voltage of the half-bridge CLLC converter at 249V. The output voltage ripple of the DC-
DC converter is 0.02 V which is approximately 0.01% voltage ripple. The output voltage can be adjusted by
controlling the switching frequency of the converter. The results obtained were within acceptable voltage
levels. Figure 10 shows the input and output resonant transformer current of the CLLC converter during
charging mode. The average output current to the load is 1.86 A.
Figure 4. DC link voltage during rectifier mode

 ISSN: 2088-8694
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Figure 5. DC link voltage during inverter mode
Figure 6. Input current at 3 phase supply during rectifier mode
Figure 7. Output current at AC side during inverter mode

1013
Figure 8. Output line-to-line voltage at AC side during inverter mode
Figure 9. Output voltage of the half-bridge CLLC resonant converter at 250V
Figure 10. Input and Output current of the half-bridge CLLC resonant transformer during charging mode

 ISSN: 2088-8694
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Overall, the results obtained for the proposed converter shows acceptable output results. The DC-
link voltage was able to maintain near 500V for both rectifier and inverter mode. For the half-bridge CLLC
resonant converter, the average output voltage across RO was obtained at 250 V. The obtained THDi for both
rectifier and inverter mode were within acceptable range of below 10%. The increase in DC-link voltage as
shown in Figure 4 is running in an open-loop control. The lack of output voltage feedback control to the
wavelet modulation strategy thus lead the result as shown in Figure 4. To improve the accuracy and
controllability of the output DC voltage, optimization to the Wavelet modulation is required such as
including voltage feedback loops. The remaining results obtained are obtained within expectations. The
desired output voltage and current of the CLLC converter were obtained in this simulation. The total
harmonic distortion for the current and the line to line voltage obtained were well within the desired range of
the proposed converter.
5. CONCLUSION
In this paper, a Wavelet modulated two-stage bidirectional AC-DC converter has been proposed for
EV charging applications. The implementation of the wavelet modulation technique for a three-phase
bidirectional AC-DC converter is based on constructing a nondyadic type MRA capable of supporting
nonuniform recurrent sampling and reconstruction of the reference DC signal and AC signal. The nondyadic
MRA was successfully constructed using a scale and shift based combined analysis and synthesis wavelet
basis functions. The simulation performance results have demonstrated that Wavelet modulation technique
can be implemented for bidirectional AC-DC converters. Most of the obtained results in the simulation were
well within expectations. However, there are still room for improving the performance of the modulation
strategy. The performance of Wavelet modulation can be further improved with the use of output voltage
feedback control for both inverter and rectifier modes.
ACKNOWLEDGEMENTS
The authors of this paper would like to thank Institute of Power Engineering, Universiti Tenaga
Nasional (UNITEN) for the financial support under the BOLD research grant, project 10289176/B/9/2017/49
and Ministry of Higher Education for the financial support under Fundamental Research Grant Scheme
(FRGS) grant, project code 20150207FRGS.
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EV Charging Systems. IEEE Transactions on Transportation Electrification. 2017;3(1):147-56.
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BIOGRAPHIES OF AUTHORS
H. K. Chiu was born in Perak, Malaysia on Dec 1989. He completed his bachelor degree
in Electrical and Electronic Engineering with University of Northumbria in 2012. He
pursued and obtained his MEng in Power Systems from University Malaya in
2015.Currently he is pursuing his PhD with College of Engineering at Universiti Tenaga
Nasional. His research interests are power electronics, electric vehicle, renewable energy
and control systems. He is also a Member of the Institution of Engineering and
Technology (IET) and the Institute of Electrical and Electronics Engineers (IEEE), and a
Graduate Member of the Institution of Engineers Malaysia (IEM).
Agileswari K. Ramasamy was born in Taiping, Perak and received her B.Sc
(Engineering) degree from Purdue University, USA in 1995 under the sponsorship of
Yayasan Tenaga Nasional. She obtained her MSc. (Control System) from Imperial
College, London in 2001 and PhD in Electrical Engineering from Universiti Tenaga
Nasional (UNITEN), under the sponsorship of UNITEN. She is currently an Associate
Professor in the Department of Electronics Communication Engineering at UNITEN and
serving as a Deputy Dean of Research and Postgraduate for College of Engineering,
UNITEN. She is also a Chartered Member of the Institution of Engineering and
Technology (IET). She is currently active in research and consultancy in control system,
power system, power quality, energy efficiency and renewable energy. She has headed
several research projects to date and has successfully published several indexed journals.
Nadia M. L. Tan received the B.Eng. (Hons.) degree from the University of Sheffield,
Sheffield, U.K., in 2002, the M. Eng. degree from Universiti Tenaga Nasional, Kajang,
Malaysia, in 2007, and the Ph.D. degree from Tokyo Institute of Technology, Tokyo,
Japan, in 2010, all in electrical engineering. Since April 2017, she has been an Associate
Professor in the Department of Electrical Power Engineering, Universiti Tenaga
Nasional. Her current research interests include power conversion systems for energy
storage, bidirectional isolated dc–dc converters, multilevel cascaded inverters for
renewable energy applications. She is a Chartered Engineer registered with Engineering
Council, United Kingdom, a Member of the Institution of Engineering and Technology
(IET) and the Institute of Electrical and Electronics Engineers (IEEE), and a Graduate
Member of the Institution of Engineers Malaysia (IEM).
Matthew Y. W. Teow received the BSc (Electronic and Electrical) degree from the
Robert Gordon University, Scotland, UK, in 1993, the MEng (Electrical) degree from
Universiti Teknologi Malaysia, Johor, Malaysia, in 1999, and the PhD (Engineering)
degree form the Multimedia University, Cyberjaya, Malaysia, in 2011.He is currently the
Head of Research Management Centre of the First City University College, Selangor,
Malaysia. His research interests include signal processing, information theory, and
machine learning. He is a Professional Engineer with Practising Certificate (PEngPC)
registered with the Board of Engineers Malaysia (BEM), Malaysia, a Chartered Engineer
(CEng) registered with the Engineering Council (EngC), UK, a Corporate Member of the
Institution of Engineers Malaysia (IEM), Malaysia, a member of the Institution of
Engineering and Technology (IET), UK, and a senior member of the Institute of
Electrical and Electronics Engineers (IEEE), US.

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