Monash University

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Topologically independent modulation of multilevel inverters

posted on 2017-01-06, 04:26 authored by Brendan Peter McGrath
The last two decades have seen an intense research effort concerning multilevel power conversion technology. This is because multilevel systems are capable of operating at high voltage levels while producing switched waveforms with low levels of spectral distortion, even at low switching rates. The development paths have considered two distinct aspects of the technology, the first being the structure of the converter topologies, while the second concerns the switching processes (i.e. modulation) that control these topologies. Not all modulation processes can be applied to all converter topologies and this is called the topological dependence of multilevel modulation methods. The prime objective of this thesis is the elimination of this dependence because this allows developments for one switching process to be applied to all topologies without differentiation.

    A general method for analytically calculating the spectral components produced by a multilevel modulation process has been developed. This technique maps the rules of a modulation process to a series of Fourier double integrals, the solutions of which represent the spectral components of the switched waveform. The use of modulation rules means that this analysis tool is ideal for the description of multilevel Pulse Width Modulation (PWM) methods with the aim of eliminating their topological dependence. It has been shown how the analysis technique can account for the effects of natural and regular sampling for both linear and non-linear modulation depths. Two approaches are proposed to solve the Fourier Double integral expressions. The first approach uses numerical integration of the outer integral terms, while the second approach uses Jacobi-Anger series expansions to develop closed form solutions for the case of sinusoidal Naturally Sampled PWM.

    The analytical method was then applied to the Phase Shifted Carrier PWM (PSCPWM) method for Cascaded inverters. This led to a mathematical understanding of the harmonic cancellation process that occurs within a Cascaded phase leg, and this allowed for the determination of the required carrier phase shift between H-Bridges to optimise the harmonic cancellation process. The mathematical results show that this cancellation is not effected by overmodulation and is not dependent on the sampling process used.
    Disposition modulation was analysed and this explained the spectral superiority of the Phase Disposition (PD) method compared to the Phase Opposition Disposition (POD) and Alternative Phase Opposition Disposition (APOD) methods. PD is spectrally superior because it places harmonic energy into a carrier component and relies on the common mode cancellation of this term when forming the line to line voltage. The other Disposition methods were shown to place spectral energy into carrier sideband terms only and so can not benefit from carrier cancellation.
    The analytical spectral performance of the PSCPWM method for Cascaded inverters, the APOD method for Diode Clamped inverters and the PWM of a Hybrid inverter were compared. When the carrier frequencies for the three PWM methods were normalised to achieve the same overall number of switching transitions the spectra were found to be identical. This result demonstrated that the modulation of Cascaded and Hybrid inverters is sub-optimal. The understanding that the PD method achieves its better performance by placing spectral energy into a carrier component which then cancels in the line to line voltage was exploited to develop a form of Bipolar Discontinuous PWM for Cascaded and Hybrid inverters. This PWM method was shown to achieve identical performance to the PD method, thus eliminating the topological dependence of the PD technique.

    Space Vector Modulation (SVM) was considered to determine if a link to carrier based modulation could be established. The optimal space vector switching sequences were determined for a Diode Clamped system based on minimising the number of switching transitions per cycle. It was found that to optimise the spectral profile of the switched waveform the middle space vectors in the switching sequence must be centered in the switching interval. Each Disposition method was examined to determine the implicit space vector sequences selected, revealing that PD is the only method that selects the same sequences as an optimal space vector modulator. A common mode injection signal was then determined for the PD technique that centers the space vector states in the half carrier period. An experimental implementation of this approach using the Bipolar Discontinuous methods for Cascaded and Hybrid inverters confirmed that this achieves equivalent SVM performance.


Campus location


Principal supervisor

Grahame Holmes

Year of Award


Department, School or Centre

Electrical and Computer Systems Engineering


Doctor of Philosophy

Degree Type



Faculty of Engineering