Journal of Engineering Science and Technology
Special Issue on Applied Engineering and Sciences, October (2014) 90 - 97
© School of Engineering, Taylor’s University

DETERMINATION OF TRIGGERING ANGLE
THROUGH A NOVEL GRAPHICAL METHOD ANALYSIS
N. F. MAILAH1,*, S. S. T. OTHMAN1, I. ARIS1,N. MISRON1, T. HANAMOTO2, H. YAMADA2
1

Department of Electrical and Electronic Engineering, Faculty of Engineering,Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Graduate School of Life Science and System Engineering, Kyushu Institute ofTechnology, Hibikino, Wakamatsu-ku, Kitakyushu, 808-0196, Japan*Corresponding Author: nashiren@upm.edu.myAbstract
This paper proposes a new graphical method analysis to determine thetriggering angle of the Neutral-Point-Clamped Multilevel Inverter (NPCMI).
The proposed graphical method analysis utilised the ideal sinusoidal waveformas the basis of the calculation. Based on the desired sinusoidal output waveformand switching state of Neutral-Point-Clamped Multilevel Inverter, triggering
angle of each switching devices are calculated and determined. The triggering
angles have been calculated for 3-level, 5-level and 7-level. Total Harmonics
Distortion (THD) values of line voltage and phase voltage are calculated andcompared and it has been concluded that this method is successfully applied
where the low THDs values are obtained.
Keywords: Neutral-Point-Clamped, Multilevel inverter, Total harmonics distortion.

1. Introduction
Multilevel Inverters are a class of inverters that utilise the concept of connecting aseries of power electronic switches in cascade. With this arrangement, the output
voltage waveform of the multilevel inverter has an equal step, staircase profile
where with the increased number of level, the more sinusoidal the output voltage
becomes. Its operation is based on the concept of synthesizing an AC output
voltage from several input DC supplies.
Nowadays, with the advancement of solid state technologies, power electronics
devices have been fabricated with higher voltage, current and power rating. Further90

Determination of Triggering Angle through a Novel Graphical Method Analysis 91

Nomenclatures
Dmn
S
VDC
VLL
VLN
VSI
V1
V5

Switching duration, deg.
Number of level
Number of odd levels
Number of sections
DC voltage, V
Line-to-line voltage, V
Line-to-neutral voltage, V
Voltage source inverter
Lower limit voltage value, VUpper limit voltage value, VGreek Symbols
Sinusoidal waveform intersection angle, deg.
αinAbbreviations
GMA
NPCMI
PWM
SHE
SVM
SVPWM
THD

Graphical method analysis
Neutral-point-clamped multilevel inverter
Pulse width modulation
Selective harmonic elimination
Space vector modulation
Space vector pulse width modulation
Total harmonic distortion

more, multilevel inverter has the advantage over the conventional two-level
voltage source inverter (VSI) by offering higher efficiency performance andreduction in production cost which are greatly sought by the industries,
particularly when dealing in high voltage and high power application.
At low voltage, low power applications, the conventional two-level voltage
source inverter are sufficient. However, the situation changes when subjected tomedium voltage, medium power and high voltage, high power applications. Byemploying Multilevel Inverter, more than two levels of output voltage can beachieved with smoother, less distortion and low Total Harmonics Distortion(THD) contents. As the number of levels of the Multilevel Inverter increases, theharmonics contents of the output voltage waveform decreases significantly [1].
Another benefit of using Multilevel Inverter is the need of the phase shifting
transformer can be avoided since the staircase steps of the output voltage is
obtained through systematically connecting the DC supply one by one into thecircuit. Also, with this Multilevel concept, each individual switches has smaller
rating which help in reducing the cost and experience lower dv/dt stresses [2].
There are three main topologies for Multilevel Inverters; Neutral-PointClamped, Flying Capacitor and H-bridge Cascade. Each of these topologies has
their own advantages and disadvantages. Low distortion, lower dv/dt stresses,
lower harmonics contents, lower switching losses and reduced electromagnetic
compatibility problems are some of the advantages of Multilevel Inverter [3]. Whilethe disadvantages are as the number of level increases, the amount of switching

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devices and other components such as capacitors and clamping diodes are also
increased, and control becomes more complicated.
The motivation for this work comes from idea to find an easier approach tocalculate the triggering angle that could produce an output voltage that has low
THD value. From the previous work of others researchers, there four major
modulation and control methods that can be applied to the Multilevel Inverter;
Carrier-Based PWM Modulation (PWM) [4], Space Vector Modulation (SVM)[5], Selective Harmonics Elimination (SHE) [6] and Space Vector Pulse Width
Modulation (SVPWM) [7].
Pulse Width Modulation was based on the comparison of a sinusoidal
reference with two carriers. In [4], the researchers proposed a method on
searching for optimal switching sequences using offset voltages.
Space Vector Modulation is a very attractive choice that is used by many
researchers. In Leon et al. [5], the authors new proposed a method of three
dimensional feed forward SVM where the actual values of the DC voltages aretaken into account in the modulation process.
In three-level inverter applications, SHE is an alternative where the harmonics
are selective selected to be eliminated based on the frequency spectrum of theoutput voltage. Franquelo et al., [6] proposed a new method called selective
harmonic mitigation PWM that generates switching patterns by using a generalpurpose random-search heuristic algorithm. In [7], a new space vector strategy
that eliminates low frequency ripple from the dc link capacitors of a three-level
converter has been proposed and verified.
The objective of this paper is to determine the triggering angle for three-phase
Neutral-Point-Clamped Multilevel Inverter through the new proposed Graphical
Method Analysis (GMA). For this purpose three levels of NPC which are 3-level, 5level and 7-level, have been investigated and tested with the proposed analysis. TheTHDs values of the output voltages were then compared with others control methods.

2. Neutral-point-clamped Multilevel Inverter
The term Multilevel Inverter basically applies to conventional three-phase bridge
configuration with an extension at the top and bottom rail of power supply. The
lowest level of Multilevel Inverter starts from three level and can be extended to
any level by adding a positive extension and negative extension for each level.
The main feature of Multilevel Inverter is it utilises the conversion of powerthrough a small increment of voltage step by synthesizing a staircase voltage fromseveral DC capacitor voltages. Neutral-Point-Clamped Multilevel Inverter has
several clamping diodes clamped to the DC capacitors rail and respective
switching devices on the phase leg as shown in Fig. 1.
Neutral-Point-Clamped Multilevel Inverter (NPC), also known as DiodeClamped was first introduced in the early 80's and has been extensively used invarious applications. This structure was first proposed by Nabae et al. [8]. One of
the advantages of this NPCMI is that when the number of levels is high, theharmonic content will be lower that the need for filters can be avoided. This NPC
also has the easiest switching control and the protection circuit required is theleast compared to the other multilevel inverter. While the major disadvantages of

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Determination of Triggering Angle through a Novel Graphical Method Analysis 93

this NPC are it is difficult to control the real power flow of the individual
converter in multilevel converter and too much clamping diodes are required
when the number of levels is high. The disadvantages also include relatively highswitching losses which limit the switching frequency to a couple hundred hertz
and unsymmetrical semiconductor loss distribution [9], the requirement of a sine
filter for standard machines [10] and the difficult extension of the voltage
converter range for use by semiconductors with higher blocking capability or aseries connection of semiconductors [11]. A NPCMI with m number of levels
characteristically comprises of (m-1) capacitors on the DC bus and voltage acrosseach capacitor is VDC/ (m-1).

Fig. 1. General Structure for Three Phase NPCMI.
Figure 2 shows the basic structure of three-phase five-level NPCMI
simulation model. In each phase leg, the forward voltage across each main powerdevice is clamped by the connection of diodes between the main power devices
and the DC capacitors rail. Table 1 below shows the switching state of five-level
NPCMI inverter. V1 is considered as lower limit and V5 as the upper limit. At
some stage in this NPC working, the switches near the neutral point are switch on
for a longer time compared to the switches further away from the neutral point.

3. Graphical Method Analysis
Graphical method analysis has been carried out for 3-level [1], 5-level [2] and 7level NPCMI with the aim of obtaining a low THDs output voltage waveform.
This method utilised the ideal sinusoidal waveform as the basis of the calculation.
For this GMA method, first the number of sections per phase leg is determinedusing the proposed Eqs. (1)-(3).

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Fig. 2. Three-Phase Five-Level NPCMI Circuit.

V1
V2
V3
V4V5

Table 1. Switching State of Five-Level NPCMI.
Sa1 Sa2 Sa3 Sa4 Sa1’ Sa2’ Sa3’ Sa4’0000111100011110001111000111100011110000

Number of sections, S per phase leg, where m is number of levels.;
S= 2 (m-1)(1)

So, from Eq. (1), for a 5-level NPC, the number of section, S is 8 where thetop section has 4 levels and bottom section also has 4 levels. Eq. (2) shows theSinusoidal Waveform Intersection angle, where n is the number of odd levels; i.e.,
1, 3, 5, … , n.
αin= sin-1 (n/S)(2)

Based on this Sinusoidal Waveform Intersection angle, the switching durationfor each IGBT at each level is calculated using Eq. (3).
Switching Duration, D;
D= 2sin-1 (n/S) ± 180°

(3)

Figures 3 and 4 show the Graphical Method Analysis for 5-level [2] and 7level for NPC Multilevel Inverter where from Eqs. (1)-(3), the duration of eachlevel are calculated and applied to each level. From the switching duration, D, theswitching angle of each level are calculated and applied to the simulation model.
Based on the equations and graphical figure, the angle of the switching have been
determined to be 250°, 195°, 165° and 110° for Level 1, Level 2, Level 3 and Level 4

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Determination of Triggering Angle through a Novel Graphical Method Analysis 95

respectively for 5-Level NPC circuit. While for 7-level NPC circuit, the switchingangles are 270°, 230°, 190°, 150°, 110° and 65° for Level 1 to Level 6 respectively.

Fig. 3. Graphical Method Analysis for 5-Level NPCMI Circuit [2].

Fig. 4. Graphical Method Analysis for 7-Level NPCMI Circuit.

4. Results and Discussion
From the calculated triggering angles and switching states, their switching
duration for each level of switches is determined. The values are then input to thesimulation model that had been designed in the Matlab/Simulink software.
Figures 5 and 6 shows the output voltage waveform for line-to-neutral voltage for
5-level NPC and line-to-line voltage NPC respectively. The THDs values of theoutput voltage are determined through the toolbox readily available in thesoftware and tabulated in Table 2. Table 3 shows the THDs values of the output
voltage for the others work of 5-level NPC.This shows that with the increment of
number of NPC levels, the THDs values of the output voltage decrease and theproposed Graphical Method Analysis is able to obtain a low THDs value of theoutput voltage.

Fig. 5. Output Voltage Waveform forLine-to-Neutral Voltage, VLN for 5-level NPCMI.
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Fig. 6. Output Voltage Waveform forLine-to-Line Voltage, VLL for 5-level NPCMI.
Table 2. THD for Different Level of NPCMI
using Proposed Graphical Method Analysis (GMA).
No. of level NPCMI
THD
(%)
VLL
VLN
IL

3-level
[1]
13.36
29.44
29.44

5-level
[2]
10.36
18.45
18.45

No. of level (CascadeH-bridge)
7-level5-level
[3]
[4]
10.31
N/A
17.06
37.80
N/A
N/A

7-level
8.18
16.00
16.00

Table 3. THDs Values of the Output Voltage
for the Others Work of 5-level NPCMI.

GMA 5-level NPCMI [2]
PWM 5-level TCHB [12]SPWM 5-level H-bridge [13]PWM 5-level cascaded [14]PWM 5-level cascaded [15]

THD of Voltage
line-to-line (VLL), %10.58

THD of Voltage
line-to-neutral (VLN), %18.62

THD of Linecurrent (IL), %
18.62

N/A

35.39

N/A

N/A

18
PDPWM
PODPWM
APODPWM

N/A
N/A

45

N/A
21.40
24.67
24.34

N/A
N/A

5. Conclusions
A low THD values for a three phase 5-level and 7-level NPCMI using new
proposed GMA has been successfully designed. The results obtained for this work
have been compared to previous work using different switching angle determinationmethod. From the comparison it showed that by using Graphical Method
Analysis, lower THD value has been achieved for three phase 5-level NPC for
both parameters, voltage line-to-neutral (VLN) and voltage line-to-line (VLL) as
well as three phase 7-level NPCMI, the THD value for voltage line-to-neutral(VLN) and line-to-line (VLL) were lower than others.

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Determination of Triggering Angle through a Novel Graphical Method Analysis 97

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Journal of Engineering Science and Technology

Special Issue 10/2014