Analytical Expression for Line Voltage THD of Three-Phase Staircase Modulated Multilevel Inverters

Eli Barbie,Alon Kuperman,Dmitry Baimel

doi:10.3390/electronics11030364

Abstract

In this article, a simple closed-form analytical expression for the line-voltage total harmonic distortion (LTHD) of three-phase staircase-modulated (SCM) multilevel inverters (MLI) is proposed. The revealed expression is valid for any conventional MLI topology with arbitrary number and parity of voltage levels. The proposed formulation is presented as an analytic function of the number of voltage levels (N) and the phase switching angles (PSA); thus, it is suited to MLIs of equal voltage source supply and of any topology. This function may be employed for accurate LTHD calculation and optimization. The results are verified against LTHD calculations and optimizations, obtained numerically from previous works. Both processor in loop (PIL)- and controller + hardware in loop (C-HIL)-based real-time experimental validations are included as well. A downloadable file containing the Maple and MATLAB functions of the proposed expression are also provided.

Highlights

The important role of three-phase (3φ) multilevel inverters (MLI) in different power conversion applications is clear [1,2,3]
In 3φ MLIs, line-voltage THD (LTHD) rather than phase voltage THD (PTHD) is of concern, since the line-voltage directly influences the load current quality [3]
Even for a known value of N, the analytic formulation of LTHD is quite peculiar, since the line-voltage of 3φ SCM-MLI is a complex stepped waveform imposed by the phase switching angles (PSA) values

Summary

Introduction

The important role of three-phase (3φ) MLIs in different power conversion applications is clear [1,2,3]. An analytical expression for the phase voltage THD (PTHD) of single-phase (1φ) SCM-based MLIs, valid for any value of N (odd and even), was recently introduced in [14]. Even for a known value of N, the analytic formulation of LTHD is quite peculiar, since the line-voltage of 3φ SCM-MLI is a complex stepped waveform imposed by the PSA values. An implicit LTHD expression, utilizing the unit-step function to represent an SCM waveform for a specific odd value of NLwuTtaiwHlsizaDsisuniggsngut7eghsgelteeeuvsdneteilitnd-3s[φti1ne1pM][1fauL1nn]Id.caAteniomndnopettlhomoeyrpreelpLdorTyienHesed[Dn9it]nfaotonr[m9pS]eCutrlMofaotpriwomenarfv,toheureftmoiolripmzthitnifemogroappalimtesicpmienewacilmiifismicez-ioarndetiicmdounvirzsaoailfvutiLeeoTnroHefpoDN-f riens7enletavteilo3nφ, wMaLsI.sAugngoethsteerdLiTnH[D4];foitrmwualsatliimoni,teudtiltioziondgdpiveacleuweisseo-freNcuarnsidvererleiepdreosennmtatainoyn, pwieacseswuigsgeetestremds.inTh[4e]s;oi-tcwallaesdl3imTHiteDd[4to] iosdindfavcatluaemsoodfifNiedanpdharseeli-evdolotangemTaHnyD,piinecwewhiicshe ttreirpmlesn. ThGeePnreorpaloizseedd LqTuaHrDterE-wxparveesssioofnSCM waveform with odd-symmetry, representing the normGaleizneedraplihzeadseqvuoalrttaegre-wwaavveesfoofrmSCsMofw3aφv-eMfoLrIms, wariethporedsde-nstyemd minetFriyg,urreepr1ecs,ednftoinrgotdhde annodrmevaleinzevdapluheasseofvNol,tacgoerrwesapvoenfodrimngs otof 3MφL-MI tLoIps,oaloregiperseosefnttheedcianscFaigduerde H1c-,bdrifdogr eod(CdHanBd) [e1v5e–n17v]aaluneds doifoNd,ec-colrarmesppeodndcionngvteortMerL(IDtoCpCo)lo[1g8ie–s20o]f pthheascea-slceagdseidlluHs-tbrraitdegdein(CFHigBu)r[e151–a1,b7,] raensdpedcitoivdeel-yc.laBmotphewdacvoensvienrtFeirgu(DreC1Cm) [a1y8–b2e0g]epnhearsaell-ylergespirlelusesntrtaetdedbyinaFuingiufireed1eax,bp,rreessspioenc[t1iv4e]:ly Equation (15) forms a generic N-level analytic LTHD expression, which is a function of PSA set α (in degrees) for any given N, which is either odd for a CHB MLI [9] or even for a DCC MLI [18]

Validation

Findings

Conclusions