An improved modulation technique suitable for a three level flying capacitor multilevel inverter

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 14, No. 3, June 2024, pp. 2522∼2532
ISSN: 2088-8708, DOI: 10.11591/ijece.v14i3.pp2522-2532 ❒ 2522
An improved modulation technique suitable for a three
level flying capacitor multilevel inverter
Khaled A. Mahafzah1
, Raneem M. Negry2
, Mohammad A. Obeidat3
, Hesham Alsalem4
1Department of Electrical Engineering, Faculty of Engineering, Al-Ahliyya Amman University, Amman, Jordan
2Electrical Mabani Company, Olaya District, Riyadh, Kingdom of Saudi Arabia
3Department of Electrical and Mechatronics Engineering, Faculty of Engineering, Tafila Technical University, Tafila, Jordan
4Mechanical Engineering Department, Faculty of Engineering, Tafila Technical University, Tafila, Jordan
Article Info
Article history:
Received Nov 2, 2023
Revised Jan 22, 2024
Accepted Jan 27, 2024
Keywords:
Grid connected PV
Multilevel inverters
Pulse width modulation
PV inverters
Switching
ABSTRACT
This research paper introduces an innovative modulation technique for control-
ling a 3-level flying capacitor multilevel inverter (FCMLI), aiming to stream-
line the modulation process in contrast to conventional methods. The proposed
simplified modulation technique paves the way for more straightforward and
efficient control of multilevel inverters, enabling their widespread adoption and
integration into modern power electronic systems. Through the amalgamation of
sinusoidal pulse width modulation (SPWM) with a high-frequency square wave
pulse, this controlling technique attains energy equilibrium across the coupling
capacitor. The modulation scheme incorporates a simplified switching pattern
and a decreased count of voltage references, thereby simplifying the control
algorithm.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Khaled A. Mahafzah
Department of Electrical Engineering, Faculty of Engineering, Al-Ahliyya Amman University
Amman, Jordan
Email: k.mahafzah@ammanu.edu.jo
1. INTRODUCTION
Direct current (DC) power to alternating current (AC) power converters play a main role in different
power system main parts: generation, transmission, distribution. These converters may also known as inverters.
Moreover, inverters are widely used in electric vehicle drives, air conditioning, variable frequency drives,
un-interruptible power supplies, high voltage DC power transmission, static var compensators, active filters,
flexible AC transmission systems, and the use of DC power sources (such as electricity generated by fuel cells,
solar panels, or batteries) [1], [2]. Inverters are classified based on the output shape for example: square wave
inverters [3], two level inverters [4], and multilevel inverters [5].
Recently, multi-level inverters (MLIs) earned a lot of attention for their benefits in different power
range applications [6]. Interestingly, MLIs can draw an input current with high power factor [7]. Also, they
have the capability to reduce the voltage stress accross the semiconductor switches as MLIs utilized several
switches in their construction [8]. Three primary topologies of multilevel inverters are: diode clamped MLIs
[9], flying capacitor MLIs (FCMLIs) [10], and Cascaded H-Bridge MLIs [11]. This paper focuses on the flying
capacitor multilevel inverters since it has lower number of diodes compared with diode clamped MLIs and
overcome the voltage balance problem of other MLIs, see Figure 1. The N level FCMLI requires (N − 1) DC
link capacitors, 2(N −1) switches and (N −1)(N −2)/2 auxiliary capacitors in each phase leg [12]. Therefore,
a single phase 3-level FCMLI comprises of 2 DC link capacitors, 4 switches, and a single auxiliary capacitor
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Int J Elec & Comp Eng ISSN: 2088-8708 ❒ 2523
as shown in Figure 1.
Sm
Sp
Sn
Sm
Cf
Vdc
C1
C2
R L
Gm
Gm
Gp
Gn
--- C:UsersuserDesktopResearch TopicsKhaled-OmidSimulationDraft3.asc ---
Figure 1. A single phase 3 level flying capacitor multilevel inverter
Many researches presented different control schemes of FCMLIs for example: in [13] authors pro-
posed a generalized approach to pulse width modulation (PWM) for an infinite number of levels, based on the
ideas of carrier swapping and phase shift. It offers a simple and straightforward technique for obtaining the
switching states, their order, and the PWM pattern. A single-phase, seven-level Gallium-Nitride GaN inverter
prototype was used for experimental testing while using MATLAB/Simulink. In [14] another level-shift PWM
method used on the flying capacitor three-phase, five-level inverter was presented. The proposed inverter has
a drawback of the suggested topology is the increased number of capacitors. 22 capacitors with 6 capacitors
connected across the switches in each phase are used. The simulation was used to confirm the phase voltage,
line voltage, and output voltage total harmonics distortion (THD).
The control of FCMLIs may also uses of model predictive control (MPC) because of its straightfor-
ward design, quick dynamic response, and accurate reference tracking. However, because it directly depends
on the system’s mathematical model to forecast the ideal switching states to be employed at the following sam-
pling time, it suffers from parametric uncertainties [15], [16]. Uncertain parameters therefore result in an MPC
that is poorly constructed. With a slight detrimental effect on the inverter’s performance, this research provides
a model-free control technique based on artificial neural networks (ANNs) to mitigate the consequences of
parameter mismatching [17], [18].
Various types of multilevel inverters find applications in the energy sector, including cascaded
H-bridge, neutral point clamped, and flying capacitor configurations [19]. In solar PV systems, a three-phase
multilevel inverter is employed alongside a brushless motor and a tracking system. Pratomo et al. [20] devel-
oped a five-level inverter incorporating a pulse width modulated controller for flying capacitors, along with an
H-bridge inverter generating five voltage levels. The use of seven-level multilevel inverters with fewer power
switches, capacitors, and gates is advocated for simplifying operations, enhancing efficiency, and increasing
reliability without complicating the control system [21]. In a study by Majdoul et al. [22], a ten-switch inverter
with up to 25 voltage levels is utilized across various applications like energy, photovoltaics, power transmis-
sion, and electric vehicles. This design aims to minimize switch losses, reduce inverter size and cost, while
ensuring good performance compared to other multilevel converter systems. Additionally, Majdoul et al. [23]
employ a nine-switch inverter without clamped diodes or flying capacitors to generate different voltage levels,
highlighting the superior harmonic performance of the clamped diode inverter [22], [23]. The adoption of a
hybrid modulation technique is emphasized across these studies for optimal control, collectively indicating
improved performance, reduced losses, and cost-effectiveness [24].
However, the control strategies discussed in the literature need an extra installations which increases
the complexity and the cost of its realization. Therefore, an enhanced modulation method for three-level
flying capacitor multilevel inverters (FCMLIs) is presented in this paper. Compared to the traditional methods,
the enhanced modulation technique is far simpler. It combines a high-frequency square wave pulse with a
sinusoidal pulse width modulation (SPWM). The two main switches (Sm) in the top and bottom of FCMLI are
An improved modulation technique suitable for a three level ... (Khaled A. Mahafzah)

2524 ❒ ISSN: 2088-8708
controlled by the square wave, which is produced at a switching frequency of 20 kHz. Positive Sp and negative
Sn switches are controlled by the square wave pulse in parallel with the comparison result of the sine wave
with the carrier signal (saw-tooth) and zero. This process ensures that the coupling capacitors are charged and
discharged equally, resulting in the achievement of energy balancing. Furthermore, which is a key component
of the flying capacitor multilevel inverters. This unquestionably contributes to maintaining the output voltage
form’s smoothness and stability as well as the inverter’s stability and dependability. The improved modulation
technique is simulated and experimentally verified.
The rest of the paper is organized as follow: the introduction to this paper is presented in section 1.
Section 2 presents a discussion of the flying capacitor multilevel inverter with conventional control strategy.
Section 3presents the improved control technique and its integration with the inverter. The simulation results
and experimental results are presented. Finally, section 4 concludes the paper.
2. FLYING CAPACITOR MULTILEVEL INVERTER: OPERATION AND CONTROL
A FCMLI see Figure 1, is a power electronic device that enables the conversion of DC power to AC
power with high voltage and low harmonic distortion. It achieves this by utilizing multiple voltage levels to
generate the desired AC waveform. The FCMLI employs a series of capacitors, called flying capacitors, which
are switched between different voltage levels to create the desired output waveform [25]. The conventional
control strategy for FCMLIs involves the use of pulse width modulation (PWM) techniques.
PWM is a widely used control method in power electronics, which allows precise control of the output
voltage or current by varying the width of the pulses in a fixed switching frequency. In the case of FCMLIs,
the PWM technique is applied to control the switching of the flying capacitors [26]. The primary objective of
the conventional control strategy is to maintain balanced voltages across the flying capacitors and achieve the
desired output voltage waveform. This is typically done by using a reference waveform generator that produces
a reference voltage waveform based on the desired output voltage. The reference waveform is compared with
the actual capacitor voltages, and the resulting error signals are used to control the switching of the flying
capacitors [27].
To achieve balanced capacitor voltages, a balancing algorithm is employed. The algorithm monitors
the voltage levels of each flying capacitor and adjusts the switching patterns to ensure that the voltage across
each capacitor remains balanced. This balancing process is crucial to ensure the efficient operation and reli-
ability of the FCMLI [27].The conventional control strategy may include other control loops to regulate the
output voltage and current, maintain the desired frequency, and protect the inverter from faults or abnormal
conditions. These control loops typically involve feedback signals from sensors or measurements of the output
voltage, current, and other relevant parameters.
It is worth mentioning that the conventional control strategy for FCMLIs has been extensively stud-
ied and developed over the years. Researchers in [28]–[32] have proposed various control algorithms and
techniques to improve the performance, efficiency, and reliability of FCMLIs. These advancements include
advanced modulation techniques, advanced control algorithms, and the integration of digital signal processors
or microcontrollers for real-time control and monitoring.
The conventional control mechanism of FCML in Figure 2 is quite complicated and large as it mainly
depends on the flying capacitor being balanced by a power signal, which is generated by the voltage across
the capacitor and the current through the capacitor, and according to the value of the power signal the voltage
state (level) are going to be chosen. The balancing of the capacitor needs an equal duration of the charging and
discharging cycle, and the developed logic can be expressed mathematically by (1):
Vref =
Vdc
2
(1)
Then, the power of the flying capacitor is given by (2):
Pfly = (
1
2
Vdc − Vfly) ∗ Ifly (2)
where Vref is the reference voltage of control loop, Vdc is the applied DC voltage, Pfly is the flying capacitor
instantaneous power, Vfly and Ifly are voltage and current in the flying.
Int J Elec & Comp Eng, Vol. 14, No. 3, June 2024: 2522-2532

Figure 2. Conventional control loop for FCMLIs
3. THE IMPROVED MODULATION TECHNIQUE: SIMULATION AND EXPERIMENTAL
The improved control method is simulated and the results are achieved using MATLAB R2020a. The
DC power supply is set to 200 V. The modulated frequency is to 50 Hz and the switching frequency is set to
20 kHz. The selected solver is ordinary differential equation (ode23tb) with a relative tolerance of 10 ms and a
maximum step size of 0.2 ms.
3.1. Simulation results
This research paper suggests an improved method of modulation technique for 3-level flying capacitor
multilevel inverter. The newly developed method is significantly simpler than conventional strategies. Four
switches are utilized to control the output wave from. Two main switches are placed at the top and bottom
of the inverter, named as Sm , they are controlled by an external high-frequency square wave at 20 kHz. The
square wave mainly contributes to the control of the positive Sp and negative Sm switches, additionally to the
comparison result of the sine wave (modulated wave) with a carrier signal (saw-tooth) and zero, according to
this positive and negative levels will be produced.
This method of operation ensures that the coupling capacitors are charged and discharged in iden-
tical amounts thus achieving energy balance. Figure 3 illustrates the block diagram of the improved control
algorithm. Sp operates in one-half of the cycle allowing energy transmission from the capacitor to the load pro-
ducing positive output voltage at the output end, meanwhile, Sn operates in the other half of the cycle allowing
energy transmission from the load to the capacitor producing negative output voltage at the output end. This
process is repeated in the same way during each cycle of the input voltage. Table 1 lists all the voltage levels
for each switching condition. For better illustration see Figure 4.
Figure 3. The improved control loop for FCMLIs

2526 ❒ ISSN: 2088-8708
Table 1. Switches’ status and load voltage
Status Sm SP Sn Vout
Mode 1 ON OFF OFF Zero
Mode 2 ON ON OFF 0.5Vdc
Mode 3 ON OFF ON −0.5Vdc
Mode 4 OFF ON or OFF ON or OFF Zero
Figure 4. Modes of operation of the improved control method
According to the previous switching states in Table 1, three modes of operation are composed as
follows:
− Mode 1: In the first operation mode (Zero state), the upper and lower main switches Sm are conducted, and
both Sm and Sp are switched off, so,the neutral point will be connected to the load, resulting in zero output
voltage across the load.
− Mode 2: In the second mode (positive state), the upper main switch Sm and the positive switch Sp are
conducted. A +V dc/2 voltage is produced at the load terminal by flowing through the following path:
C1-upper Sm-Sp-Load.
− Mode 3: In the third operation mode (negative state), the lower main switches are switched on, and the cur-
rent will flow through the following path. C2-lower Sm-Sn-Load, producing an output voltage of −V dc/2
at the output end of the MLI.
The simulation of the the improved control technique is illustrated in Figure 5. The figure depicts that
both upper and lower switches Sm are triggered on or off simultaneously. Moreover, the other two switches are
gatted on or off according to the sign of the modulated sine wave. The positive switch SP is on during positive
half cycle. In contrast, the negative switch Sn is on during the negative half cycle. To show the effectiveness
of the improved control technique, the single phase 3 level FCMLI is simulated using the control proposed in
Figure 3. The simulated load voltage is shown in Figure 6. As expected the load voltage has three different
voltage levels: 0.5 Vdc, Zero, and -0.5 Vdc. Lastly, to ensure the energy balance of the 3 level FCMLI controlled
by the improved control technique, the voltage across both DC link capacitors are plotted in Figure 7. As seen
in Figure 7, each DC link capacitor has the same DC voltage (0.5 Vdc) during the steady state operation of the
3 level FCLI.
3.2. Experimental results
To evaluate the efficacy of the proposed control approach, a comprehensive experimental setup was
developed using the SPICE tool. Figure 8 illustrates the configuration, which incorporates two function gen-
erators. These generators produce a sinusoidal waveform with a peak to peak voltage of 5 V at a frequency of
50 Hz and a saw-tooth signal with a peak to peak voltage of 5 V at a frequency of 20 kHz. Additionally, two
12 V DC power sources are integrated into the system.

To generate pulse width modulation (PWM), the sinusoidal and the saw-tooth signals undergo a com-
parison process. The comparison is carried out using two LM358P operational amplifiers (OP-Amps) config-
ured as comparators. The higher comparator generates the PWM signal, while the lower one determines the
positive and negative halves of the modulated signal (representing the sign of the sine wave). Notably, during
the negative half of the sinusoidal wave, the comparators remain inactive. To rectify this, a diode bridge rec-
tifier is employed, ensuring a comprehensive evaluation of the signal. The rectified voltage is then compared
with the saw-tooth signal to finalize the modulation process.
Figure 5. The output of the improved control technique
Figure 6. Load voltage of a single phase 3 level FCMLI
The LM358P operational amplifier is a widely utilized integrated circuit, serves a pivotal role in this
setup. As a dual operational amplifier with low power consumption and high gain, the LM358P is adept at
various signal processing tasks, including amplification, filtering, and signal conditioning. Its wide voltage
operation range makes it adaptable to different power supply levels, coupled with a high input impedance
and low output impedance, facilitating efficient signal transfer between stages. Moreover, the LM358P boasts
a versatile input and output voltage range, rendering it suitable for both single-ended and differential signal
applications. The LM358P operational amplifier continues to contribute significantly to the advancement of
electronic circuits and applications, owing to its reliability, versatility, and cost- effectiveness.

2528 ❒ ISSN: 2088-8708
Figure 7. The average and absolute voltage across the DC link capacitors
Figure 8. Test setup
Due to omitting the negative half cycle of the modulated signal, a new compensation stage has been
added to the test setup. This stage uses an extra AND gate to confirm the negative sign. The modulated signal,
saw-tooth, PWM and positive sign detection results are shown respectively in Figure 9. For the negative sign
detection, the previous discussion would be repeated. As expected, the positive and negative switches are both
gated using the pulse train shown in Figure 10. It is seen that, each switch is operated during half of sine-wave
period.

As a result, the experimental section shows the simplification of applying the control loop of the
proposed modulation technique. The proposed technique reduces the number of control loops from two (con-
ventionally) to only one simple loop. The output voltage of a three-level flying capacitor multilevel inverter
approves the effectiveness of applying the proposed modulation technique. Importantly, the energy balance of
the coupling capacitors due to voltage balance across them is an important justification of proposing the im-
proved modulation technique. At this stage of the research, the proposed modulation technique is only applied
for the three-level FCMI and the use of this method for higher level is left for future research.
Figure 9. Waveforms: modulated wave, saw-tooth wave, PWM and positive sign detection
Figure 10. Waveforms: positive and negative switches’ pulses
4. CONCLUSION
This paper proposed a novel efficient control modulation strategy for a three-level FCMLI. Distin-
guished by its user-friendly nature, this approach offers simplicity compared to traditional methods by integrat-

2530 ❒ ISSN: 2088-8708
ing SPWM with a high-frequency square wave pulse. Operating at a frequency of 20 kHz, this square wave
pulse manages both primary switches (Sm) positioned at the top and bottom of the FCMLI. The control mech-
anism involves the parallel utilization of the square wave pulse with the comparison outcome of the sine wave
against the carrier signal (saw-tooth) and zero, governing the positive Sp and negative Sn switches. Notably,
the proposed modulation technique can be implemented using logic ICs, amplifiers, and resistances, which
makes it a very simple and promising technique. The technique ensures equal charging and discharging of
coupling capacitors, achieving energy balance. Furthermore, the enhanced technique ensures energy balance
across the flying capacitor, a pivotal component of the FCMLI, by maintaining equal charge and discharge for
each capacitor during every operational cycle. This methodology simplifies control and modulation techniques,
reduces component count, and mitigates challenges in maintaining voltage balance across flying capacitors. In
the experimental section, the paper illustrates the simplification of the control loop in the proposed modulation
technique. The method reduces the number of control loops from the customary two to a single, straightfor-
ward loop. The validation of the proposed modulation technique is demonstrated through the output voltage
of the three-level flying capacitor multilevel inverter. This not only contributes to the inverter’s stability and
reliability but also ensures a smooth and constant output voltage. The simulation and implementation of the
enhanced technique are provided and discussed in detail.
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10.3311/PPee.21879.
BIOGRAPHIES OF AUTHORS
Khaled A. Mahafzah received a B.Sc. degree and M.Sc. degree in electrical power engi-
neering from the Department of Electrical Power Engineering at Yarmouk University, Irbid, Jordan,
in 2010 and 2012, respectively. From 2012 to 2014 he served as a research and teaching assistant
at the Energy Engineering Department at German Jordanian University. In 2014 he started his Dr.
Techn., (Ph.D.) in power electronics and drives at the Electric Drives and Machines Institute at Graz
University of Technology, Austria. Currently, he is associate professor of power electronics and
drives in Electrical Engineering Department at Al-Ahliyya Amman University. His research interests
are in power electronics, electrical drives, and the integrity of renewable engineering sources with
power systems. He can be contacted at email: k.mahafzah@ammanu.edu.jo.
Raneem M. Negry received a B.Sc. degree in electrical engineering from Al-Ahliyya
Amman University, Amman, Jordan, in 2023. She worked as research assistant trainee in Energy
and Smart Grids Research Lab at the University of Bradford, Bradford, United Kingdom. Currently,
she is energy efficiency engineer trainee at Electrical Mabani Company, Riyadh, Saudi Arabia. Her
research interests are in power electronics, smart grids, power system optimization. She can be
contacted at email: raneemnegry@hotmail.com.

2532 ❒ ISSN: 2088-8708
Mohamad A. Obeidat (Member, IEEE), received the B.Sc. degree in electrical engineer-
ing from the Jordan University of Science and Technology, Jordan, in 1999, the M.Sc. degree in
electrical engineering from Yarmouk University, Jordan, in 2006, and the Ph.D. degree in electrical
engineering from Wayne State University, in 2013. He is currently a Professor in the Department of
Electrical Power and Mechatronics Engineering and Vice-Dean of Scientific Research and Faculty
of Graduate Studies, Tafila Technical University. He demonstrated excellent research and academic
abilities and professional potentials. He has published several articles in the field of electrical en-
gineering. His research interests include the field of intelligent control systems, renewable energy,
intelligent systems, and mechatronics. He can be contacted at email: maobaidat76@ttu.edu.jo.
Hesham Alsalem he obtained PhD degree in mechanical engineering from Wayne State
University, Detroit, MI, (USA) in 2016. He obtained a master’s degree in mechanical engineering
from Jordan University of Science and Technology (Jordan) in 1999. And his bachelor degree in
mechanical engineering from Jordan University of Science and Technology (Jordan) in 1996. His
research interests are in the fields of automotive engineering, energy harvesting systems, electrical
and hybrid vehicles, electrical motors, inverters and batteries, and lithium sulfur batteries. He teaches
several bachelor-level courses for mechanical engineering/hybrid vehicle technology students. He
can be contacted by email at: hmanasreh 10@ttu.edu.jo.

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