# A Review of Modular Multilevel Converters for Stationary Applications
## 4 MMC Modulation Techniques  
Various pulse width modulation (PWM) techniques have been developed to generate a desired output voltage for the MMC. These modulation techniques, depending on the switching frequency, can be classified as high switching frequency PWM (HSF-PWM), low switching frequency (LSF-PWM), and fundamental switching frequency (FSF-PWM) modulation scenarios [3; 5]. The semiconductor switching losses increase with the switching frequency. As a result, the high switching frequency method is generally utilized when a small number of submodules are employed, whereas low switching frequency and fundamental switching frequency schemes are preferred when substantial submodules are involved [4]. Carrier-based PWM is a typical HSF-PWM method in which, for multilevel converters, the modulation reference of each phase is compared with multiple carrier waveforms to create the gating signals [34]. Triangular or sawtooth waveforms are prevalently applied as the compared carrier signals. The reference signals are produced by involving application-oriented control strategies, for example, voltage-oriented control (VOC) and field-oriented control (FOC), and they can be given as [77]  
\[v_{x}=m\times\frac{V_{dc}}{2}\sin(\omega t+\varphi_{x}) \tag{32}\]  
where \(v_{x}\) is the phase modulation reference, \(m\) is the amplitude of modulation index in the range [0, 1], \(\omega\) is the fundamental angular frequency, and \(\varphi_{x}\) is the phase angle of {0, 2\(\pi\)/3, 4\(\pi\)/3}. Carrier-based modulation schemes, based on the arrangement of multiple carriers, are categorically divided as phase-shifted carrier-based (PSC-PWM) and level-shifted carrier-based (LSC-PWM) techniques [117], as seen in Figure 15. In PSC-PWM, \(N\) identical triangular carrier waveforms are employed and displaced horizontally with a phase shift 2\(\pi\)/\(N\). By comparing the modulation signals with the \(N\) carrier signals, the MMC can produce an output voltage with \(N\)+1 levels. The carrier waveforms in the upper and lower arm can be arranged with an interval angle \(\pi\)/\(N\), with which the power converter can generate (\(2N+1\))-level output voltage [43; 118]. The latter approach reduces the harmonic distortion of the output voltage with approximately double voltage levels at the cost of additional computation burden. Thanks to the independent modulation signal for each submodule, the PSC-PWM method imposes equal-distributed power stresses and switching losses on the semiconductors and contributes to the submodule capacitor voltage balancing [119]. The PSC-PWM approach is widely used in the multilevel power conversion system. Using LSC-PWM, it produces (\(N\)+1)-level output voltage at the AC side involving \(N\) carrier signals with uniform magnitude and frequency disposed sequentially in line with zero axis [120; 121]. The LSC-PWM strategy has three subfamily members including phase-disposition (PD-PWM), phase-opposition-disposition (POD-PWM), together with alternate phase-opposition-disposition (APOD-PWM). The different modulation techniques are illustrated in Figure 16. Although the LSC-PWM approach can be easily implemented to produce multilevel voltage, it is less preferred in the MMC application, since it causes uneven voltage distribution across the submodule capacitors, which results in a higher harmonic distortion of output voltage and leads to an increase of circulating currents. To overcome this situation, a series of rotation techniques regarding carrier or reference signals, e.g., a carrier rotation technique [122], a modified carrier rotation technique [123], or a signal rotation technique [120], are proposed to equally arrange submodule capacitor voltage. Furthermore, the optimized PD-PWM are developed with a selective loop bias mapping technique [124] or interleaving angle method [125] to reduce total harmonic distortion and balance submodule capacitor voltage naturally. The switching frequency of space vector modulation (SVM) falls into the category of the LSF-PWM scheme.