12-07-2014, 12:46 PM
Selective Harmonic Elimination Technique for a
Multilevel Inverter
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Abstract
— For a multilevel inverter, switching angles at
fundamental frequency are obtained by solving the selective
harmonic elimination equations in such a way that the
fundamental voltage is obtained as desired and certain lower
order harmonics are eliminated. As these equations are nonlinear
transcendental in nature, there may exist simple, multiple or even
no solutions for a particular modulation index. Previous work
has shown that if iterative numerical techniques are implemented
to solve the transcendental equations, only one solution set is
obtained even there may exist multiple solution sets; other
suggested approaches such as resultants method, theory of
symmetric polynomial produce all possible solution sets, but
these methods are more computationally complex. In this paper a
new approach is presented to implement the Newton-Raphson
method for solving the transcendental equations which produces
all possible solutions with any random initial guess and for any
number of levels of multilevel inverter. Among multiple solution
sets obtained, the solutions which produce least THD in the
output voltage is chosen. As compared with the single set of
solution, the decrease in the THD can be up to 3% in case of
multiple solution sets. The computational results are shown
graphically for better understanding and to prove the
effectiveness of the method. An experimental 11-level cascade
multilevel inverter is employed to validate the computational
results.
I. INTRODUCTION
multilevel inverter is more recent and popular type of
power electronic converter that synthesizes a desired
output voltage from several levels of dc voltages as inputs. If
sufficient number of dc sources is used, a nearly sinusoidal
voltage waveform can be synthesized.
In comparison with the hard-switched two-level pulse
width modulation inverter, multilevel inverter offers several
advantages such as, its capabilities to operate at high voltage
with lower dv/dt per switching, high efficiency and low
electromagnetic interference [1]-[4].
To synthesize multilevel output ac voltage using different
levels of dc inputs, semiconductor devices must be switched
on and off in such a way that desired fundamental is obtained
with minimum harmonic distortion. The commonly available
switching technique is selective harmonic elimination (SHE)
Jagdish Kumar is a Research Scholar in Electrical Engineering
Department, Indian Institute of Technology Roorkee-247667, India (emailjkb70dee@
iitr.ernet.in).
Biswarup Das is an Associate Professor in Electrical Engineering
Department, Indian Institute of Technology Roorkee-247667, India (emailbiswafee@
iitr.ernet.in).
Pramod Agarwal is a Professor in Electrical Engineering Department,
Indian Institute of Technology Roorkee-247667, India (emailpramgfee@
iitr.ernet.in).
method at fundamental frequency, for which transcendental
equations characterizing harmonics are solved to compute
switching angles [2], [3]. It is difficult to solve the SHE
equations as these are highly nonlinear in nature and may
produce simple, multiple, or even no solutions for a particular
value of modulation index. A big task is how to get all
possible solution sets where they exist using simple and less
computationally complex method. Once these solution sets are
obtained, the solutions having least THD are chosen.
In [4]-[6], iterative numerical techniques have been
implemented to solve the SHE equations producing only one
solution set, and even for this a proper initial guess and
starting value of modulation index for which solutions exist
are required. In [7], [8], theory of resultants of polynomials
and the theory of symmetric polynomials has been suggested
to solve the polynomial equations obtained from the
transcendental equations. A difficulty with these approaches
is that for several H-bridges connected in series, the order of
the polynomials become very high thereby making the
computations of the solutions of these polynomials very
complex. Optimization technique based on Genetic Algorithm
(GA) was proposed for computing switching angles for 7-level
inverter in [9]. The implementation of this approach requires
proper selection of certain parameters such as population size,
mutation rate etc, thereby its implementation becomes also
difficult for higher level inverters. To circumvent above
problems, in this paper the application of the Newton-Raphson
method for solving these equations is proposed. The proposed
technique is implemented in such a way that all possible
solutions for any number of H-bridges connected in series are
computed for any arbitrary initial guess with negligible
computational effort. A complete analysis for an 11-level
inverter using five H-bridges per phase in series is presented,
and it is shown that for a range of modulation index ,
switching angles can be computed to produce the desired
fundamental voltage V1 = (s 4Vdc/) while eliminating 5th,
7th, 11th, and 13th harmonic components. For demonstrating the
validity of the proposed methods the results obtained by
computations are compared with experimental results.
VII. CONCLUSION
The selective harmonic elimination method at fundamental
frequency switching scheme has been implemented using the
Newton-Raphson method that produces all possible solution
sets when they exist. In comparison with other suggested
methods, the proposed technique has many advantages such
as: it can produce all possible solution sets for any numbers of
multilevel inverter without much computational burden, speed
of convergence is fast etc. The proposed technique was
successfully implemented for computing the switching angles
for 7-level and 11-level CMLI. A complete analysis for 11-
level inverter has been presented and it is shown that a
significant amount of THD reduction can be attained if all
possible solution sets are computed.