INTRODUCTION
Recently, many reports were talking about the disadvantages of the normal
single inverters or two level inverters especially due to high voltage
change rates dv/dt, which produced a commonmode voltage across the motor
winding and power electronics switches. Multilevel converters were introduced
to overcome this problem. A multilevel inverter converts the electric
power from dc to ac form by synthesizing desired sinusoidal voltage from
a series of singlephase, full bridge (Hbridge) inverter units. Separate
dc sources are required to supply such inverter, which may be obtained
from batteries, fuel cells, or solar cells or from one dc source synthesizing
a combination state of diodes or capacitors, for high power application
(Tolbert et al., 2002). Multilevel converter can be operated without
using a high frequency technique of Pulse Width Modulation (PWM), which
has the disadvantage of electromagnetic interference with communication
signals and produces high stress on the switches at the high voltage application
(Rashid, 2004). Unlike diode clamed and flyingcapacitor inverters, cascade
multilevel inverter needs the least number of components to achieve the
same number of voltage level. Cascade multilevel converters have wide
applications especially for Highpower Electrical Vehicle (HEV) motor
drives because it can be used to convert small dc voltage to high ac voltage.
High frequency switching can exacerbate the problem because of the numerous
times that commonmode voltages should impress upon the motor each cycle.
The main problems reported were motor bearing failure and motor winding
insulation breakdown because of circulating current, dielectric stresses,
voltage surge and corona discharge (Corzine and Familiant, 2002). Multilevel
inverters overcome these problems since individual switching devices have
much lower dv/dt per switching and they operate at high efficiencies since
these devices switch on and off at a much lower frequency than PWM  controlled
inverter system (Tolbert et al., 1999). The multilevel voltage
source inverter is a unique structure that allows them to reach high voltages
with low harmonics. For this reason, multilevel inverters can easily provide
the high power required for a large electric drives.
Cascade Multilevel Inverter
The cascade Hbridge inverter consists of a number of single phase
Hbridge units with or without PWM techniques. Figure 1 shows Hbridge
unit and its voltage waveforms, while Fig. 2 shows the construction of
a single phase cascaded inverter. The main function for each Hbridge
is increase the voltage level and to control the width of its output as
shown in Fig. 3. Each Hbridge has its conducting angle (α), which
means that each Hbridge can produce output waveform with different width.
The summation of output voltages of all H bridges produces the final
out voltage of the system with low harmonics.

Fig. 1: 
Hbridge unit 

Fig. 2: 
Cascade multilevel circuit 

Fig. 3: 
Synthesis of the output voltage 

Fig. 4: 
Schematic diagram of transformer multilevel cascaded inverter 
The cascade Hbridge multilevel inverter uses a separate dc source for each
Hbridge; at any time, the output of each Hbridge has one of three discrete
levels; positive, negative or zero, adding them together results in a staircase
waveform, V_{an} as shown in Fig. 3. The schematic diagram of transformer
type multilevel cascaded inverter is shown in Fig. 4. This type usually
used in practice to eliminate the high number of dc supplies required to
supply each H Bridge separately and for this reason this type has been
chosen in this study.
Harmonics Eliminations Method
Choosing appropriate conducting angles for the Hbridges can eliminate
a specific harmonic in the output waveform (Rashid, 2004). The required
conduction angles can be calculated by analyzing the output phase voltage
of cascade inverter assuming that four Hbridges have been used, the output
voltage V_{a0} can be given as:
V_{a0} = V_{a1}+V_{a2}+V_{a3}+V_{a4}+V_{a5}
.. 
(1) 
Since the wave is in symmetry along the xaxis, both Fourier coefficient
A_{0} and A_{n} are zero. Just the analysis of B_{n}
is required.
j 
= 
Number of dc sources 
n 
= 
Odd harmonic order 
Therefore, to choose the conducting angle of each Hbridge precisely, it
is necessary to select the harmonics with a certain amplitude and order,
which needs to be eliminated. To eliminate 5th, 7th and 11th, harmonics
and to provide the peak fundamental of the phase voltage equal to 80% of
its maximum value, it needs to solve Eq. 3, with modulation
index M = 0.8.
Solution of this set of nonlinear transcendental equations can be achieved
by using numerical methods such as NewtonRaphson method. Table
1 shows a set of conduction angles which produce a minimum harmonics
contents, with different modulation indices.
Minimizing Total Harmonic Distortion
To minimize the THD the following procedure can be followed. The conducting
angle to give a certain value of the THD can be determined as follows
(Feng et al., 1998):
Taking the partial derivative of the THD,
The conducting angle for minimum value of THD can be obtained.
Simulation of the System
Pspice/orcade software has been used as a tool to simulate the circuit
which consists of single phase rectifier and the inverter circuit with
and without transformer. Figure 5 shows the simulation result of output
voltage for the diode clamped transformer cascade inverter.
Table 1: 
Sets of the conducting angles with different modulation indices 

Figure 6 shows the analysis of frequency spectrum of
the output voltage waveform and it is clear from the figure that the harmonics
with order 5th, 7th and 11th have been eliminated and this gives advantage
of the multilevel to reduce the total harmonic distortion more with out
implementing PWM technique. Reduction of harmonics content means that
the THD has lower value. This feature of multilevel inverter meets the
requirement of the high power applications which can be provided with
high voltage output and low THD and this can be achieved by adjusting
the Hbridge conduction angle to eliminate the high amplitude harmonics.
Experimental Result
To verify the validity and superiority of the multilevel inverter, a hardware
laboratory prototype model has been constructed which consists of four fullsingle
phase bridge inverter units, four cascaded transformers with the same size.
Low cost microprocessor PIC16F877A has been used to generate required signal
to control the entire system. Figure 7 shows block diagram
of the hardware system. Figure 8 demonstrates the experimental
output voltage of the inverter, with 50 Hz and modulation index of 0.8.
Using the method minimizing harmonic with iterative process can provide faster
solution to calculate the THD for large number of steps. It has been found in
the simulation that the THD is equal to 7.51% and in experiment is 8.39% for
the same output voltage. And these values can be reduced further if the number
of H bridges increases. This result confirms the superiority for the multilevel
inverter with the best result recorded for the PWM inverter topology as 19.7%
(Tolbert et al., 2002; Lai and Feng, 1996).

Fig. 5: 
Output voltage of transformer cascade multilevel inverter


Fig. 6: 
Frequency spectrum analysis of multilevel wave form 

Fig. 7: 
Block diagram of system hardware 

Fig. 8: 
Cascade multilevel inverter output at M = 0.8 and f = 50 Hz 
Although the transformer is considered as bulky and loose component but
utilization of its leakage inductance gives us higher order of harmonic
elimination, also the isolation between each bridge is guaranteed.
CONCLUSION
In this study the cascaded multilevel inverters have been investigated.
Multilevel transformer type with only one dc supply has been chosen. Software
model has been developed using Pspice soft ware. Simulation and experimental
voltage waveforms have been obtained and compared which showed a close
agreement between them.
Reduction of harmonics and THD value has been achieved easily with out using
PWM technique. This can be obtained if the conduction angles of single phase
Hbridges are properly chosen. It has been found in the simulation that THD
is equal to 7.51% and in experiment is 8.39% for the same output voltage; these
values are much lower than PWM inverter. With this control strategy of multilevel
cascaded switches, it is possible to construct high power drives with high output
voltage and low harmonics or THD.