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Simple Time Averaging Current Quality
Evaluation of a Single-Phase Multilevel PWM
Inverter
Abstract:
This paper addresses theoretical calculation of a single-phase multilevel PWM
inverter current Total Harmonic Distortion (THD). Analytical approach introduced
in late 1980s for a 2-level inverter is generalized for an arbitrary level count
for a single-phase inverter. Though the obtained closed-form piece-wise analytical
solutions assume (infinitely) large ratio of switching and fundamental frequencies
and pure inductive load, they are practically very accurate for the ratios of
(apparent) switching and fundamental frequencies larger than 25-30 and
inductance dominated loads. Along with strict mathematical solutions suggested
are simple accurate Bessel function approximation and hyperbolic average trend
one. The formulas clearly reveal a single-phase PWM inverter current THD
dependence on modulation index for an arbitrary voltage level count and are
easily modified to cover grid-connected cases.
Existing system:
 Multilevel inverters are being widely used for medium/high voltage and
other applications. Over the past 15 years, power electronics research
community has shown significant interest in multilevel current THD
analysis.
 The annual quantity of journal and conference papers dealing with
multilevel converter voltage and current THD exceeds 100 in total. Many
recent multilevel inverter papers end up with current THD evaluation results
that are typically based on current frequency spectra numerical calculations/
measurements (FFT).
Proposed system:
 In the proposed system, the approach is applied to a single-phase multilevel
PWM inverter current quality that is evaluated in time domain using current
ripple Normalized Mean Square (NMS) criterion. Current NMS can be
further easily converted into current THD.
 For an arbitrary number of voltage levels, a solution for current ripple NMS
is piece-wise analytical and employs only elementary functions. The
delivered estimates are asymptotic in the sense that the ratio of two
frequencies - (apparent) PWM and fundamental - is assumed (infinitely)
large and, thus, the current ripple NMS depends on modulation index only.
 Current ripple NMS is obtained by double time integration (averaging) of a
normalized current ripple square - on a PWM period and on a fundamental
one - that may be roughly understood as the time domain equivalent of the
frequency domain double Fourier transform.
Circuit diagram:
Reference:
[1] J. Rodriguez, S. Bernet, Bin Wu, J.O. Pontt, and S. Kouro, ”Multilevel
voltage-source-converter topologies for industrial medium-voltage
drives,” IEEE Trans. Ind. Electron., vol. 54, no. 6, pp. 2930-2945, Dec.
2007.
[2] J. Rodriguez, L.G. Franquelo, S. Kouro, J.I. Leon, R.C. Portillo, M.A.M
Prats, and M.A. Perez, ”Multilevel converters: an enabling technology for
high-power applications,” IEEE Proceedings, vol. 97, no. 11, pp. 17861817, Nov. 2009.
[3] L.G. Franquelo, J. Rodriguez, J.I. Leon, S. Kouro, R. Portillo, and M.A.M.
Prats, ”The age of multilevel converters arrives,” IEEE Ind. Electron.
Magazine, vol. 2, no. 2, pp. 28-39, June 2008.
[4] S. Kouro, M. Malinowski, K. Gopakumar, J. Pou, L.G. Franquelo,
Bin Wu, J. Rodriguez, M.A. Perez, and J.I. Leon, ”Recent advances
and industrial applications of multilevel converters,” IEEE Trans. Ind.
Electron., vol. 57, no. 8, pp. 2553-2580, Aug. 2010.