Harmonic Analysis of a Modular Multilevel Converter Using Double Fourier Series

  • Quach, Ngoc-Thinh (Dept. of Electrical Engineering, Jeju National University) ;
  • Chae, Sang Heon (Dept. of Electrical Engineering, Jeju National University) ;
  • Ahn, Jin Hong (Dept. of Electrical Engineering, Jeju National University) ;
  • Kim, Eel-Hwan (Dept. of Electrical Engineering, Jeju National University)
  • Received : 2016.10.20
  • Accepted : 2017.10.07
  • Published : 2018.01.01


This paper presents a harmonic analysis of the modular multilevel converter (MMC) using a double Fourier series (DFS) algorithm. First, the application of DFS for harmonic calculation in the MMC is made by considering the effect of arm inductor. The analytical results are then confirmed by comparing with the simulation results of using the fast Fourier transform (FFT) algorithm. Finally, distribution of harmonics and total harmonic distortion (THD) in the MMC will be analyzed in three cases: harmonics versus number of levels of MMC, harmonics versus total switching frequency and harmonics versus modulation index. The simulation results are performed in the PSCAD/EMTDC simulation program in order to verify the analytical results obtained by Matlab programming.

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Fig. 1. Configuration of the MMC: (a) Circuit diagram, (b) Submodule

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Fig. 2. Phase-shifted PWM method for the MMC

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Fig. 3. Conventional PWM method and 2-D model of DFS

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Fig. 4. Equivalent circuit of the MMC

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Fig. 5. Analytical results and simulation results: (a) Analyticalresults, (b) Simulation results with simulation timestep of 0.5 μs, (c) Simulation results withsimulation time step of 10 μs

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Fig. 6. Voltage drop on arm inductor

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Fig. 7. Distribution of harmonics versus number of levelsof MMC (fct = 3600 Hz). (a) 5-level MMC, (b) 11-level MMC, (c) 21-level MMC

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Fig. 8. Total harmonic distortion versus number of levels ofMMC

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Fig. 9. Distribution of harmonics versus total switchingfrequency (11-level MMC): (a) fct = 1800 Hz, (b) fct= 3600 Hz, (c) fct = 5400 Hz

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Fig. 10. Total harmonic distortion versus total switchingfrequency

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Fig. 11. Harmonic profile of 11-level MMC

Table 1. The parameters of MMC

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Table 2. THDs of the ideal and real line-to-line voltages

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Supported by : Korea Institute of Energy Technology Evaluation and Planning (KETEP)


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