On the modeling of MMC for use in large scale dynamic simulations

Abstract

Abstract-This paper focuses on simplified models of the Modular Multilevel Converter suitable for large-scale dynamic studies, in particular simulations under the phasor approximation. Compared to the existing literature, this paper does not a priori adopt the modeling approach followed for the original twolevel or three-level Voltage Source Converter. On the contrary, a model is derived following a physical analysis that preserves its average internal dynamic behavior. An equivalent control structure is proposed and various alternatives are highlighted. The proposed model with its controllers has been implemented in a phasor simulation software and its response has been validated against a detailed Electromagnetic Transient model. Finally, an illustrative example is presented with the application of the proposed model on a large grid consisting of AC areas interconnected with a multi-terminal DC grid.

Modeling of MMC for Fast and Accurate Simulation of Electromagnetic Transients: A Review

“…Based on the assumption of the identical construction of submodules and instantaneous voltage balance control, Refs. [20,101,106,107] represent all N submodules in an arm by an equivalent module. Despite their idealistic assumptions, these models inherently capture internally-stored energies and are suited for large signal analysis of the MMC.…”

“…• Average arm SFM (AVM): This model incorporates the switching effect by utilizing a discrete set of values for the insertion index using module level modulation, which improves accuracy [22,23] Moreover, further simplified models for MMC have been proposed in the literature [19][20][21][22]31,[107][108][109][110][111][112][113][114][115][116][117][118]. The works in [19][20][21][22] extend the classical average modeling technique for 2/3-level converters [119] to MMC and represent its terminal dynamics using controlled sources; [107,[111][112][113][114]120] present enhanced versions of this model that incorporate the blocked state of operation for DC fault simulations and/or consider the effects of distributed submodule capacitor voltage ripple in MMC's terminal dynamics.…”

Tuning of control loops for grid-connected Modular Multilevel Converters under a simplified port representation for large system studies

“…the voltage at the upper and lower arms). After this mathematical operation the energy equations in abc are added and divided by 3, following the procedure shown in [5,9]. This variable can be used to accurately represent the power balance between the dc and ac interfaces of the converter in a simplified way.…”

“…For both of the tuning strategies, a simplified model of the MMC suited for large-power-system oriented studies is being considered, where only the interface variables at the dc-and ac-side are taken into account in addition to the governing power balance associated to the converter distributed energy storage, following what has been presented in [5,9,12].…”

Avoiding AC/DC grid interaction in MMC based MTDC systems

“…Nonetheless, since the present work is oriented at large-power system studies, where the macroscopic behavior of the converter is favored over a detailed representation of all its internal dynamics, a simplified small-signal model of the MMC is preferred. More precisely, the work is based on the approach presented in [6,7], where only the aggregated dynamics of the zero sequence circulating current (or the dc current) and the total energy stored in the capacitors of the MMC are modelled, besides the dynamics of the ac-side active and reactive currents. It was shown in [6], that if the modulation indices for the MMC arms are calculated to compensate for the voltage oscillations in the internal equivalent arm capacitor voltages, this approach results in an accurate representation of the acand dc-side terminal behavior, while limiting the need for representing the internal variables.…”