Real Time Harmonic Elimination Using a
Modified Carrier
Hirak Patangia
College of Engineering & Information Technology
University of Arkansas
Little Rock, USA
e-mail: hcpatangia@ualr.edu
Sri Nikhil Gupta Gourisetti
College of Engineering & Information Technology
University of Arkansas
Little Rock, USA
e-mail: gigupta@ualr.edu
Abstract— The paper proposes a harmonic elimination
technique that is based on comparison modulation with a
modified carrier. Typically, selective harmonic elimination
method calculates the switching angles offline using iterative
computations and programmed into a digital processor. Here
we are advancing a modulation-based harmonic elimination
technique to remove the unwanted harmonics. It is a novel
PWM method where a reference sinusoid with the desired
signal frequency is compared against a modified carrier signal
with the same time period as the reference. Simulation and
laboratory studies are included.
I. INTRODUCTION
There exists a vast amount of literature related to
harmonic elimination in power electronics. Sinusoidal pulse
width modulation (SPWM) is a well-known method to
eliminate lower order harmonics in modern inverter control
[1]. Here a sinusoidal reference is compared against a high
frequency triangular carrier to produce the PWM switching
signal as shown in Fig. 1a. A frequency ratio of 10:1 or
greater virtually eliminates all lower order harmonics as
shown in the FFT of Fig. 1b.
V tri V control
t
t
V (t) pwm
Fig.1a Sine Triangle PWM (SPWM)
Fig.1b SPWM Spectra (fc = 10fref, fc = Carrier frequency)
__________________________________________________________
The work was partially supported by NSF (Grant #0942327)
Selective harmonic elimination (SHE) is another method
popular in motor control that results in lower switching
frequency [2, 3]. Here the switching times are chosen in such
a way that the unwanted harmonics except the fundamental
are eliminated. The harmonic elimination problem boils
down to solving a set of transcendental equations which are
solved off line using iterative computations. The switching
times are programmed into a look up table in a digital
processor and to be read in real time. To avoid the need for
solution of complex transcendental equations offline, recent
research activities for harmonic elimination have been
focused toward modulation based harmonic elimination [4,
5]. This has the advantage of real time comparison of the
reference with a modified carrier to produce the desired
PWM signal. The generation of the modified carrier reported
in [4] is complex since it requires fast digital computation on
the fly and D/A conversion. A digital signal processor is
required for its implementation. In the present work, we are
formulating a simplified modulation based harmonic
elimination technique without the need for ‘on the fly’ signal
processing. The method produces a well-defined comparing
signal and the resulting comparison with a sinusoidal
reference produces the PWM signal similar to sine-triangle
PWM with suppression of the undesired harmonics. The
fundamental is tunable while suppressing the undesired
harmonics. The paper reports the preliminary finding which
is novel and appears to have some attractive features. The
motivation for the work originated from our original desire
to develop low cost switching modulators which have lower
switching frequency for RF application [6].
II. SINE-SINE PWM
The most common PWM that eliminates lower order
harmonics is sine-triangle. As seen in Fig. 1b, the first
appreciable harmonic (carrier sideband) appears at f
c
– 2f
o
,
where f
c
is carrier switching frequency and f
o
is reference
frequency. If higher f
c
is acceptable, the sideband
components can be pushed out easily. For lower f
c
, it is
necessary to remove the sidebands to allow more baseband
space. The Fourier coefficients of the sine-triangle SPWM
are complex in nature since it involves Bessel functions [1]
and often simulation is used to verify the nulling of the
harmonics. For simplicity and ease of harmonic elimination,
we begin the proposed method with a sine-sine PWM. Here,
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