This paper proposes a harmonic reduction approach for a pulse width modulation (PWM) ACAC converters using Bee Colony Optimization (BCO). The optimal switching angles are provided by BCO to minimize harmonic distortions. The sequences of the PWM switching angles are considered as a technical constraint. In this paper, simulation results from various optimization techniques including BCO, Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are compared. The test results indicate that BCO can provide a better solution than the others in terms of power quality and power factor improvement. Lastly, experiments on a 200W ACAC converter confirm the performance of the proposed switching pattern in reducing harmonic distortions of the output waveform.
I. INTRODUCTION
In modern applications of power electronics, voltage adaptability of the energy supply is increasingly required. The ACAC converter has become a major component in various types of control equipment such as heating, lighting and motor speed controllers. Energy efficiency improvement techniques also need soft start control and power factor correction regulated by the variable voltage converters replacing regular fixed AC sources
[1]
. In general, phase angle control is used for voltage adaptation. In addition, average output voltage can be controlled by varying the thyristor firing angle
[2]
. The phase angle control approach has many advantages. For example, it can be conveniently implemented and exhibits cost effectiveness for large scale applications. However, the delay of the firing angle causes discontinuation of the power flow and significant harmonics to both the input and output sides.
For an alternative solution, a PWM AC chopper is suggested for an AC voltage controller. Using the chopping technique, the AC voltage signal is modified as a PWM signal to regulate the output voltage. This approach can provide nearly sinusoidal current and voltage waveforms. In addition, it can improve both power factor and power quality. Since the switching frequency is limited by the switching losses in high power and high voltage applications, harmonic filter techniques are required to eliminate the low harmonic components caused by low frequency choppers.
The harmonic elimination methods used in AC choppers are similar to those employed in PWM inverters
[3]

[8]
. The general technique is that the waveform is analyzed in the frequency domain using Fourier approaches. In addition, the NewtonRaphson technique is adopted to solve nonlinear equations with the iterative computation. Recently, stochastic search techniques have been widely applied to solve complex and nonconvex optimization problems. For related applications, the switching angles of the PWM pattern are obtained by various heuristic approaches including genetic algorithm (GA), particle swarm optimization (PSO), and artificial neural network (ANN)
[9]

[19]
. All of the mentioned techniques aim to minimize the total harmonic distortion (THD) of the converter and to provide an optimal solution.
A branch of nature inspired algorithms known as swarm intelligence is focused on insect behavior such as Ant Colony Optimization (ACO). Recently, Bee Colony Optimization (BCO) was proposed by Karaboga in 2005
[20]
. The BCO algorithm is a very simple and robust stochastic optimization algorithm when compared with previous algorithms. In addition, it is a novel and attractive approach for application in the power electronic area.
In this paper, an optimal switching strategy based on BCO for PWM ACAC converters is proposed. BCO is adopted to provide the optimal switching angles of the PWM pattern. The proposed approach aims to minimize the harmonic distortion of converter’s output waveforms with satisfying technical constraints of the switching angle sequences. Results from previous works are compared in this paper. In addition, an experiment with a 200W ACAC converter is used to confirm the performance of the proposed switching pattern in terms of reducing the harmonic distortions of the output waveform.
This paper is organized as follows. Section II describes the background of PWM ACAC converters and presents the BCO concept. Section III expresses the problem formulation of the optimal switching strategy. Section IV proposes the BCO algorithm to provide the optimal PWM switching patterns. Sections V and VI shows the simulation and experimental results, respectively. And the last section concludes the paper.
II. BACKGROUND
 A. PWM ACAC Converters
The power circuit configuration of a PWM ACAC converter is shown in
Figure 1
(a). Switch
S_{1}
controls the power delivered to the load and switch
S_{2}
is the freewheeling path to transfer energy to the load when switch
S_{1}
is turned off.
PWM AC chopper. (a) Power circuit configuration. (b) PWM pattern, waveforms of output voltage/current and input current.
In a conventional PWM AC chopper, the switching pattern is regularly fixed. This conveys the low order harmonics to the input and output waveforms. A harmonic elimination technique is an adaptation of the switching angles to reduce the waveform distortion. In
Figure 1
(b), improved input and output waveforms are shown. Using this technique, the total harmonic distortion is also reduced. In this paper, the optimal switching angles for the PWM ACAC converter are provided by stochastic search approaches.
In the PWM chopper approach, the output voltage is controlled by the switching pattern. Thus,
M
pulses are required for a quarter of a sinusoidal cycle. In addition, switch
S_{1}
is turned on at different switching angles
α_{1}
,
α_{2}
, ...
α_{M}
turned off at angles
β_{1}
,
β_{2}
, ...
β_{M}
Using the Fourier series expression, the output voltage can be written as:
Where
n
=1,2,3...
By considering only the odd components of the waveform in (1), the output voltage can be written as:
Where
n
=1,3,5...
The fundamental coefficient
A
_{1}
is expressed as:
The harmonic coefficient
A_{n}
is expressed as:
Where switch
S_{1}
is turned on at various switching angles
α_{1}
,
α_{2}
, ...
α_{M}
and turned off at
β_{1}
,
β_{2}
, ...
β_{M}
, where
M
is the pulse per quarter cycle.
The total harmonic distortion of the load current and voltage are defined as:
Where
n
= 3,5,7...
 B. Bee Colony Optimization
Bee Colony Optimization (BCO) mimics the intelligent behaviors of honey bees and it was proposed by Karaboga in 2005
[20]
. The BCO algorithm has an advantage in providing global optimal solutions. In addition, it has the capability of solving difficult combinatorial optimization problems.
A colony of bees for the collection and processing of nectar consists of two groups: scout bees and worker bees. The scout bees are responsible for searching for sources of nectar, while the worker bees are responsible for loading the nectar to the hive. The processes of the intelligent behaviors of scout bees can be summarized as follows:

Scout bees seek the sources of nectar in different directions and return to the hive.

After that, the scout bees dance to inform the quality, quantity, direction and distance of the food supply.

Then, the colony of bees decides to send worker bees to bring nectar to the hive.
This bee behavior is converted to a heuristic search algorithm including the steps of initialization, search, evaluation and update. The BCO algorithm applied to the optimal switching problem is described in Section IV.
III. PROBLEM FORMULATION
Here, the optimal switching pattern problem for PWM ACAC converters is formulated as an optimization problem. The objective of the function is to minimize the THD expressed as:
Subject to:
Where
A
_{1}
is the fundamental coefficient of the output voltage,
V_{o,ref}
is the reference output voltage,
β_{M}
is equal to
π
/2, and
M
is number of pulse per quarter cycle of the PWM waveform. The boundary of each switching angle can be determined with a simple calculation. For example, at
M
=3, the fixed interval
ϕ
is equal to
π
/6. Thus, the boundaries of the switching angles are as follows:
The optimization model described in equations (7) and (8) is used to design a converter to reduce harmonic distortions. It requires an efficient optimizer to solve the problem as formulated. In the next section, a solution algorithm based on BCO is described.
IV. PROPOSED SOLUTION ALGORITHM
In this section, the BCO algorithm to provide optimal PWM patterns is shown in
Figure 2
and described as follows:
Proposed BCO algorithm.
Step 1: Specify the BCO parameter as shown in
table 1
and the AC voltage controller such as
M
and
V_{o}
.
PARAMETER OF BCO
Step 2: Randomly generate the initial populations (
N
) of the switching angles,
α
and
β
, while satisfying the constraints using the following equations:
Where
i
= 1 to
M
.
Step 3: Evaluate the fitness value of the initial population and arrange the fitness in descending order using the fitness function as:
Where
F
is described in (7). For dealing with the constraint, the violated angle is adjusted to the nearest boundary.
Step 4: Select S best solutions for the neighborhood search.
Step 5: Separate the
S
best solutions into two groups (
E, SE
), and determine the size of neighborhood for each best solution. Note that neighborhood sizes are equal to
NE
for solution group
E
and
NO
for solution group (
SE
).
Step 6: Generate solutions around the selected solutions within the neighborhood sizes (
NE, NO
) and evaluate the fitness value from each patch.
Step 7: Select the best solution from each patch.
Step 8: Check the stopping criterion. If the algorithm is not stopped, increase the iteration.
Step 9: Assign the new population (
NS
) to generate new switching angles. Then, return to Step 3.
V. SIMULATION RESULTS
The PWM ACAC converter is designed and simulated using two different software packages. First, the proposed BCO algorithm is implemented in the MATLAB environment to provide the optimal switching angles for the converter. Second, the designed PWM chopper is simulated by PSpice software with system parameters of
V_{i}
= 220 V,
f
= 50 Hz,
R_{o}
= 240 Ω,
L_{o}
= 300 mH and
M
= 3 pulses. For the BCO algorithm, the required parameters are listed in
table I
. The BCO parameters are selected from an empirical examination with a reasonable cost of computation. This affects both the convergence characteristic and computational efficiency.
 A. Optimal Switching Angle Solution
The optimal switching angles, obtained by the proposed BCO algorithm at various output voltage levels, are shown in
table II
.
OPTIMAL ANGLES OBTAINED BY PROPOSED METHOD AT VARIOUS DESIRED OUTPUT VOLTAGE
OPTIMAL ANGLES OBTAINED BY PROPOSED METHOD AT VARIOUS DESIRED OUTPUT VOLTAGE
 B. Convergence Characteristic
Based on multiple runs of the simulation, BCO can provide optimal solutions with very little variation. The selected convergence solutions are shown in
Figures 3
and
4
. The solutions converge within 5 iterations. The minimum
THD_{v}
is 0.1574. The mean and standard deviations of the solutions are 0.1616 and 0.0139, respectively.
Solution convergence from the proposed BCO approach.
Converter parameters versus output voltage using GA [13], PSO [16] and proposed BCO PWM. (a) Output voltage THD, (b) input current THD. (c) Input power factor.
 C. Comparative Results
The performance of the designed converter is investigated with different optimization techniques. Both the input and output parameters of the converter such as the current and voltage THD, and the power factors are shown. In the test, the output voltage of the converter is 160 V. Test results from the proposed BCO, PSO and GA algorithms are compared in
table III
. The results indicate that BCO can provide a better solution than the other approaches in reducing voltage and current harmonics and improving the input power factor. It should be noted that the displacement power factor (DPF) is a power factor without considering harmonic distortions.
PERFORMANCE OF THE GA, PSO, AND BCO AT OUTPUT VOLTAGE = 160 V
PERFORMANCE OF THE GA, PSO, AND BCO AT OUTPUT VOLTAGE = 160 V
Fig. 4
shows the performance of the proposed BCO PWM technique when compared to GA and PSO results.
Figure 4
(a) shows the
THD_{v}
versus the output voltage. The results show that the
THD_{v}
of the proposed BCO PWM technique is lower than the results from the other techniques. And
Figure 4
(b) compares the results of the
THD_{i}
from both techniques. The simulation results indicate that the
THD_{i}
from the proposed BCO PWM technique is lower than the results from the other PWM techniques. In
Figure 4
(c), a profile of
PF_{i}
against the output voltage is shown. It indicates that the proposed BCO PWM technique can effectively enhance the input power factor of the power source.
VI. EXPERIMENTAL RESULTS
Here, an experiment on the PWM AC chopper is used to confirm the performance of the proposed technique. The system parameters used in the experiment are similar to the ones used in the simulation. The implemented laboratory prototype is shown in
Figure 5
.
Experimental equipment.
A PIC 16F628A microprocessor is adopted to generate the PWM for controlling the gate signals of the switching devices. The converter can vary the output voltage in the range of 20220V. Here, the output voltage is set at 140 Vrms to make a comparison between simulation and experimental results. The input and output waveforms are shown in
Fig. 6
and
7
, respectively. The results indicate a significant correlation between the simulation and the experiment. In addition,
Fig. 8
shows the experimental harmonic spectra of the output voltage when compared to the simulation. From the expanded harmonic spectra, the low frequency harmonics are a lot less. Thus, eliminating higher frequency harmonics can be done effectively using a regular low pass filter.
Waveforms of output current and voltage. (a) Simulation results. (b) Experimental results (voltage, 100 V/div, current, 1 A/div.)
Waveforms of input current and voltage. (a) simulation results and (b) experimental results (voltage, 100 V/div, current, 1 A/div).
Spectra of output voltage compared between experiment and simulation results.
VII. CONCLUSIONS
This paper proposes a harmonic reduction technique based on BCO for single phase PWM ACAC converters. The optimal PWM switching angles are obtained by the proposed BCO algorithm. From the test results, BCO can provide a better solution than GA and PSO in minimizing total harmonic distortions. In addition, the simulation and experimental results are correlated to confirm the performance in terms of improving power the quality and power factor. The proposed approach can be applied to design optimal switching patterns for other power converter topologies.
BIO
Wanchai Khamsen was born in Lampang Province, Thailand, in 1974. He received his B.S. degree in Technical Education from the Rajamamgla Institute of Technology, Thailand, in 1997, his M.Eng. degree in Electrical Engineering from King Mongkut’s Institute of Technology North Bangkok, Bangkok, Thailand, in 2003, and his Ph.D. degree from Mahasarakham University, Maha Sarakham, Thailand, in 2013. He is currently working as an Assistant Professor for the Faculty of Engineering, Rajamamgla University of Technology Lanna, Lampang, Thailand. His current research interests include ac choppers, converter systems for improving power quality, power factor and optimization techniques.
Apinan Aurasopon was born in Amnat Charoen Province, Thailand, in 1971. He received his B.Eng. degree in Electronic Engineering from Northeastern College, Khon Kaen, Thailand, in 1995, his M.Eng. and Ph.D. degrees in Electrical Engineering from King Mongkut’s University of Technology Thonburi, Bangkok, Thailand, in 2003 and 2007, respectively. He was a Lecturer in the Department of Electrical Engineering, Faculty of Engineering, Burapha University (BU), Chonburi, Thailand, in 2007. He was transferred to the Faculty of Engineering, Mahasarakham University (MSU), Maha Sarakham, Thailand, in 2008, where he is currently an Assistant Professor. His current research interests include softswitched converters, ac choppers, converter systems for improving power quality, and the application of electronics and computer to agriculture.
Chanwit Boonchuay received his D.Eng. degree in Electric Power System Management from the Asian Institute of Technology (AIT), Khlong Luang, Thailand, in 2011. He was a Visiting Scholar at the Center for Electrical Energy System (CEES), of Hong Kong, Hong Kong, China, and the Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA, in 2009 and 2010, respectively. He is currently the Head of the Center for Electrical and Embedded System Technology (CEEST), Rajamangala University of Technology Rattanakosin, Prachuap Khiri Khan, Thailand. His current research interests include artificial intelligence applications, power system optimization, power system restructuring and deregulation, risk management in energy markets, distributed generation, and smart grids.
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