applsci-11-00538

applied
sciences
Article
Power Quality Analysis of the Output Voltage of AC Voltage
and Frequency Controllers Realized with Various Voltage
Control Techniques
Naveed Ashraf 1, Ghulam Abbas 1,* , Rabeh Abbassi 2and Houssem Jerbi 3
Citation: Ashraf, N.; Abbas, G.;
Abbassi, R.; Jerbi, H. Power Quality
Analysis of the Output Voltage of AC
Voltage and Frequency Controllers
Realized with Various Voltage
Control Techniques. Appl. Sci. 2021,
11, 538. https://doi.org/
10.3390/app11020538
Received: 27 November 2020
Accepted: 5 January 2021
Published: 7 January 2021
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1Department of Electrical Engineering, The University of Lahore, Lahore 54000, Pakistan;
[email protected]
2Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi Arabia;
r[email protected]
3Department of Industrial Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi Arabia;
[email protected]
*Correspondence: [email protected] or [email protected]
Abstract: Single-phase and three-phase AC-AC converters are employed in variable speed drive,
induction heating systems, and grid voltage compensation. They are direct frequency and voltage
controllers having no intermediate power conversion stage. The frequency controllers govern the
output frequency (low or high) in discrete steps as per the requirements. The voltage controllers
only regulate the RMS value of the output voltage. The output voltage regulation is achieved on the
basis of the various voltage control techniques such as phase-angle, on-off cycle, and pulse-width
modulation (PWM) control. The power quality of the output voltage is directly linked with its
control techniques. Voltage controllers implemented with a simple control technique have large
harmonics in their output voltage. Different control techniques have various harmonics profiles
in the spectrum of the output voltage. Traditionally, the evaluation of power quality concerns is
based on the simulation platform. The validity of the simulated values depends on the selection of
the period of a waveform. Any deficiency in the selection of the period leads to incorrect results.
A mathematical analytical approach can tackle this issue. This becomes important to analytically
analyze the harmonious contents generated by various switching control algorithms for the output
voltage so that these results can be successfully used for power quality analysis and filtering of
harmonics components through various harmonics suppression techniques. Therefore, this research
is focused on the analytical computation of the harmonics coefficients in the output voltage realized
through the various voltage and frequency control techniques. The mathematically computed results
are validated with the simulation and experimental results.
Keywords: voltage and frequency controller; grid voltage compensation; power quality; PWM
control; harmonics coefficients
1. Introduction
1.1. Problem Statement
Power quality is one of the major concerns in today’s modern power system. In tradi-
tional generation and distribution systems, the issue of low power quality is meaningless as
the connected load is linear such as incandescent lamps and heating load. The speed of the
rotating loads is governed via their voltage control that is achieved through conventional
approaches. That includes the use of auto-transformers, transformer tap-changing mecha-
nisms, and variable resistance. These power control mechanisms are inefficient and are
replaced with switching converters nowadays. The power electronic converters are plying
a vital role in the development of modern-day life by converting one form of electric power
into another form. The converted output in the power conversion process is not always
Appl. Sci. 2021,11, 538. https://doi.org/10.3390/app11020538 https://www.mdpi.com/journal/applsci

Appl. Sci. 2021,11, 538 2 of 24
in the pure form and includes unwanted components called harmonics. The nature of
unwanted harmonics deteriorating the power quality should be known before employing
different harmonics mitigation and compensation methods. This research focuses on the
mathematical computation of the harmonic components analytically and then the valida-
tion of mathematically computed results through simulation and experimental results.
1.2. Literature Review
Reference [ 1 ] pin-points that the source of the harmonics in the power system is owing
to the use of non-linear loads that include battery charging system, smart refrigerating and
air-conditioning systems, computers, electric furnaces, and fluorescent or LED lighting
systems. The current drawn by the non-linear loads or devices is non-linear which leads to
poor power quality issues. This non-linear current to be supplied by the input source flows
through the entire power system. This may interact with the capacitance and inductance
of the system. Therefore, the generated harmonics is one of the major concerns and
challenging issues that leads the male functioning of the connected and protection systems,
and reliability concerns of devices and components in the power system [ 2 ]. They also
increase the neutral current in a three-phase power system [ 3 ]. They become more serious
once they interact with the grid or system’s inductance. Therefore, this problem is a major
resonance source for poor power quality and instability concerns in the power system.
All industrial consumers are forced to improve their produced negative footprint through
power compensating topologies. Therefore, the harmonic analysis becomes one of the main
concerns for performance evaluation of the power converting systems.
The profile of the generated harmonics in the power conversion process is directly
linked with the type and switching algorithm of the power processing units. The power
quality of the grid or load voltage may be improved through the harmonic elimination
techniques. The generated harmonics may be tackled at the unit level or system level [ 4 , 5 ].
Normally, passive [ 6 , 7 ] and active filters [ 8 – 11 ] are employed to suppress them. The selec-
tion of cutoff frequency or bandwidth depends on the frequency of the dominant harmonics.
The harmonics elimination through passive filter approaches is normally employed in low
power to medium power applications as they are simple and reliable. Here, the basic key
is to divert the unwanted components or block them through a high impedance. These
techniques may include series, parallel or hybrid filters. In parallel filter techniques, the
propagation of generated harmonics is blocked to move towards the source by establishing
a low impedance path across the load. In series compensating techniques, harmonics are
blocked due to the high impedance of series compensators. The harmonics suppression
through traditional DC link capacitors is bulky and unreliable and therefore, this approach
is not cost-effective. These issues are tackled in the slim type DC link capacitors as reported
in [ 12 ]. Here, the magnitude of the harmonics is only evaluated without considering their
phase. Their harmonics suppression characteristics at the system level are not improved
as they may be achieved with traditional power converting topologies realized with DC
or AC filters (choke). The power converting topologies realized with slim type DC link
capacitors have improved harmonics suppression capabilities once they are connected in
parallel with other power converters. In the AC to DC conversion process, the higher pulse
rectifier’s topologies may also be employed but their use is restricted to some applications
due to their complex circuit arrangement [ 13 – 16 ]. The mathematical computation of output
voltage and input current harmonics of a six-pulse rectifier is reported in [ 17 ] but they are
not practically validated. The harmonic profile of various outputs of power converting
systems is practically evaluated in [1,18].
The variation in the magnitude and phases of harmonics is observed due to the use of
a DC-link capacitor or DC and AC chokes [ 19 , 20 ]. It is investigated in [ 21 ] that the phase
angles of the three-phase and single-phase for the fifth harmonic are equal and opposite at
the unit level. But there may be some variation in their phase once the number of power
converting systems is connected to the same coupling point. The harmonics suppression
through the paralleling of power converters requires a large number of power converters.

Appl. Sci. 2021,11, 538 3 of 24
This approach cannot be employed in the case where a converter is feeding power to an
individual load.
The direct AC-AC converters are more attractive over the sizeable indirect AC-AC
converters (AC-DC-AC converters) as their operation is accomplished through single-stage
power conversion. They are the more viable choice in most applications, such as motor
speed drive, grid voltage compensation [ 22 – 24 ], and induction heating systems [ 25 , 26 ].
Thyristor-based AC voltage controllers are used at the domestic level for speed regulation
of the fans. They are also employed in some industrial drives. These topologies are simple
to implement but they have certain serious drawbacks. The RMS values of the output
voltage are controlled via the control of the firing delay. They have a problem of low order
harmonics as the switching frequency is equal to the input source. That increases the
total harmonic distortion (THD) and reduces the power factor (PF). On-off cycle control
is another approach to control the output RMS voltage with the load having a high time
constant. For example, heavy industrial load having a high mechanical time constant, or
heating load having a high thermal time constant. This voltage control topology is also
realized with thyristor-based converters. Here the switching of a thyristor is accomplished
at zero crossings of the input voltage. The amplitude of the fundamental component
and generated harmonics depends upon the number of on and off cycles. The generated
harmonics also exist at low frequencies that cannot be easily suppressed. The generated
harmonics are shifted at higher frequencies in the power converter implemented with
the pulse-width modulation (PWM) approach by increasing the switching frequencies
of operating devices [ 27 ]. The high-frequency harmonics can be easily eliminated by
employing a low pass filter. The output voltage regulation is governed through the
duty cycle control of the PWM signals. The AC voltage controller operated with bipolar
voltage gain may regulate the output frequencies in discrete steps. This is accomplished
by operating the converters in non-inverting and inverting modes according to the output
frequency requirements [25,26].
The output voltage and frequency control are realized through various switching
schemes and converting topologies. Each switching scheme or power converting topology
has a distinctive harmonic profile. Conventionally, the harmonic analysis based on FFT is
employed in [ 28 – 31 ] for harmonic analysis but it has the problem of aliasing and spectrum
leakage as it is based on sampling frequency and window. The selection of the period of
the wave is also a critical issue and it leads to incorrect results. The double Fourier series
is employed in the Jacobi matrix [ 32 ] but its spectrum analysis is inaccurate as only two
frequencies from the input, output, and sampling are considered. This problem is tackled in
the triple Fourier series as in [ 33 ] but this approach is not mature due to some deficiencies.
These approaches are employed in indirect AC-AC converters and cannot be employed in
direct AC-AC converters due to complex mathematics. The harmonics of an uncontrolled
three-phase rectifier are computed through sample delta and state-space approach in [ 34 , 35 ]
but these approaches are complex to apply in other power converting topologies. A novel
approach for harmonic analysis is reported in [ 36 ] for a rectifier circuit realized through a
multi-pulse approach. Here the three input phase currents are converted in the form of a
stepped wave by employing the paralleling of four converters. The harmonics contents
of each converter are suppressed through their elimination topologies. The harmonics
contents of AC-AC converters are usually addressed in Simulink’s dependent environment.
1.3. Research Contribution
Existing mathematical tools that are employed to explore the power quality concerns
of the inverters (DC-AC converters) become complicated if they are used in power quality
concerns of direct AC-AC converters. An accurate analytical and simple approach that
we call pulse selective approach (PSA) as reported in [ 17 , 26 ] is employed to compute
the harmonic contents for AC-DC converters and direct frequency changers but they are
not yet practically validated. In this approach, a waveform that apparently seems to be
non-sinusoidal is decomposed to its parents’ sinusoidal components during some selected

Appl. Sci. 2021,11, 538 4 of 24
periods of time. The power quality concerns of each sinusoidal wave in the selected period
are evaluated; then their results are merged to have the harmonic contents of that entire
waveform. According to the authors’ best knowledge, this approach is not employed for
power quality evaluation in the direct single-phase and three-phase AC voltage controllers.
Therefore, in this research article, the harmonics contents of the output voltage for various
AC voltage control schemes are analytically computed. The computed harmonics contents
are validated through practical and simulation results. The MATLAB/Simulink based
environment is employed to simulate the harmonics contents for direct AC-AC converters
by carefully selecting the period as an inaccurate selection of the period of a waveform
leads to inaccurate results. In a nutshell, the contribution of this research article is the suc-
cessful application of the proposed (analytical) pulse selective approach to AC-AC voltage
converters for computing harmonic contents and then the validation of mathematically
computed results through simulation and experimental results.
1.4. Paper Organization
The arrangement of this research article includes the description of the pulse selec-
tive approach (PSA) in Section 2, followed by the harmonics coefficients computation in
Sections 3–5. Section 6validates the computed values with the results obtained through
simulation and practical values. The conclusion is explored in Section 7.
2. Pulse Selective Approach
This analytical approach is one of the simplest methods to evaluate the power quality
concerns of current or voltage waveforms that apparently seem to be non-sinusoidal or
complex. The non-sinusoidal nature of waveforms is due to the switching mechanism
involved in the switching converters. That may invert, non-invert, or chop the input
voltage waveform at the output in a single-phase supply system. This may also be due to
the summation or subtraction of the input voltage sources at the output in a three-phase
supply system. Thus, it results in harmonic contents. So, a resultant non-sinusoidal voltage
or current waveform is a series of various harmonic frequencies.
In the pulse selective approach (PSA), such non-sinusoidal current or voltage wave-
forms are decomposed into their parent sinusoidal components. Then each component is
analyzed for its period that is required to compute its harmonic coefficients. The harmonic
coefficients of each sinusoidal component present in the considered (current or voltage)
waveform are computed. The harmonic coefficients of all sinusoidal components are added
by the superposition principle to have the harmonic coefficients of a complete waveform.
This way, well-distinct numerical expressions of non-sinusoidal currents and voltages are
obtained to compute the harmonics. The steps involved in the PSA are presented in the
form of a flow chart shown in Figure 1.
It should be remembered that the selection of a period is quite crucial. For example, in
the case of direct AC-AC and AC-DC converters, the period of the input voltage waveform
is always ‘2 π ’, but the periods of the output voltage or current waveforms may or may
not be ‘2 π ’. To add more insight, the outputs of the frequency controllers for double
and half frequency become periodic after ‘ π ’ and ‘4 π ’ intervals respectively. For these
outputs, the period of the required components is equal to the period of the instantaneous
waveform but this is not always true. For example, the voltage waveform where the
required output frequency is three times the input voltage frequency, the period of the
required component (voltage component having frequency three times the input frequency)
and instantaneous output voltage waveform is one third and is equal to the period of the
input voltage waveform respectively. The periods of these sinusoidal components are
chosen by analyzing them for zero average value during selected periods.
As can be seen, the PSA needs not to involve look-up tables, Bessel functions, and
numerical techniques for the computation of harmonic magnitude and angle. Realizing this
fact, the application of PSA to compute the harmonic contents of non-sinusoidal current
and voltage waveforms of AC-AC voltage controllers is presented in the coming sections.

Appl. Sci. 2021,11, 538 5 of 24
The harmonic coefficients for other types of switching converters can also be computed by
PSA. Switching mechanism, converter type (single-phase or three-phase), input and output
waveform frequencies, and so on result in different current and voltage waveforms.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 27
input voltage waveform respectively. The periods of these sinusoidal components are cho-
sen by analyzing them for zero average value during selected periods.
As can be seen, the PSA needs not to involve look-up tables, Bessel functions, and
numerical techniques for the computation of harmonic magnitude and angle. Realizing
this fact, the application of PSA to compute the harmonic contents of non-sinusoidal cur-
rent and voltage waveforms of AC-AC voltage controllers is presented in the coming sec-
tions. The harmonic coefficients for other types of switching converters can also be com-
puted by PSA. Switching mechanism, converter type (single-phase or three-phase), input
and output waveform frequencies, and so on result in different current and voltage wave-
forms.
Figure 1. Flow chart of the pulse selective approach (PSA).
Figure 1. Flow chart of the pulse selective approach (PSA).
3. Single-Phase AC Voltage Controllers
They have many control techniques to regulate the RMS value of the output AC
voltage. Their detailed and analytical analysis is explored below.