This article presents three dynamic linear state space models of Modular Multilevel Converter (MMC) which are suitable for small-signal dynamic studies and controller design. The three models differ by the number of states (two, six and ten) and therefore are suitable for different applications based on the required accuracy. The 2 nd and 6 th order models ignore dynamics of the second harmonics and circulating current suppression control. The main challenges of dynamic analytical modelling of MMC are the non-linear multiplication terms in equations for modulating oscillating signals. The multiplication non-linear terms is therefore considered directly in the rotating DQ frame. This requires simultaneous modeling in zero sequence, fundamental frequency DQ and double fundamental frequency DQ2 frames. The proposed linear analytical models are implemented in state-space in MATLAB. The validity and accuracy of the models are verified against detailed 401 level MMC model in PSCAD/EMTDC in both: time and frequency domains. The results show very good accuracy for the 10 th order model and decreasing accuracy for the lower order models.

This paper presents model for Modular Multilevel Converter (MMC) in phasor format, which is convenient for power flow and parameter studies. The model is derived in rotating dq coordinate frame, and the coordinate frame at double the fundamental frequency, in steady-state. A substantial analytical basis is presented in order to facilitate direct mathematical manipulations of non-linear terms in the rotating frame. An 8 th order model is firstly derived which includes circulating current representation. Later, the circulating current suppression controller (CCSC) is modelled and the magnitude of second harmonic control inputs is studied. The final model for MMC with CCSC is given in a simple and convenient form for power flow studies. The accuracy of the proposed models is verified against a detailed dynamic MMC benchmark model in PSCAD. Finally, a comparison between the MMC model and 2level VSC model is given.

High power DC/DC converters and DC hubs are required to interconnect the high-voltage direct current (HVDC) systems with different voltage levels. Low frequency 50/60 Hz modular multilevel converters (MMCs) are known to provide better power quality, higher reliability, and lower switching losses compared to conventional two-level voltage source converters (VSCs). This study presents the optimal design of an MMC VSC for medium frequency applications suitable for DC/DC converters and DC hubs. The design aims at minimising the MMC total power loss, size, and weight as these are great importance for HVDC converters. The optimal values for the main MMC parameters including cell capacitance, arm inductance, number of cells, and operating frequency are determined using an in depth study carried out in Matlab and PSCAD. The effect of different voltage balancing methods on converter performance is also investigated. It is shown that a number of cells within the range of 20-56 with an operating frequency around 300 Hz/500 Hz for onshore/offshore applications give best trade-off between converter total loss and overall size and weight.

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This paper presents a systematic study on designing hybrid direct current (DC) circuit breaker (CB) based on fast thyristors. As an illustration, the DC CB main parameters are calculated for a 120kV, 1.5kA test breaker with interrupting current of 10kA. The studies indicate that the opening time of 2.3ms can be achieved only if fast thyristors are employed. It is further illustrated that there is a design tradeoff between minimum interrupting current capability and discharge time for the internal capacitors (reclosing speed). The DC CB control system for opening and closing is presented based on different levels of protection and the self-protection. The DC CB is modelled in PSCAD and simulation results are used to evaluate the breaker performance under different operating conditions. It is concluded that the model represents well the DC CB and can be employed for DC grid protection studies. It is further shown that opening time becomes longer as interrupting current reduces, and it is very long in case of load current interruption.