This paper presents a new state-space model (SSM) to represent the four types of currents flowing through a Modular Multilevel Converter (MMC). In line with the converter topology, the model itself is modular. In other words, its configuration adapts itself to the number of AC phases, to the active or passive nature of the AC-side grid, to the connection between the AC and DC neutral points, and to the number of submodules. The model describes the influence of the MMC arm voltages on the currents using an average behavior of the submodules. Simulations performed using a software dedicated to electrical engineering systems demonstrate the value and the accuracy of the proposed model.

In highly fragmented and relatively stable cold-seep ecosystems, species are expected to exhibit high migration rates and long-distance dispersal of long-lived pelagic larvae to maintain genetic integrity over their range. Accordingly, several species inhabiting cold seeps are widely distributed across the whole Atlantic Ocean, with low genetic divergence between metapopulations on both sides of the Atlantic Equatorial Belt (AEB, i.e. Barbados and African/European margins). Two hypotheses may explain such patterns: (i) the occurrence of present-day gene flow or (ii) incomplete lineage sorting due to large population sizes and low mutation rates. Here, we evaluated the first hypothesis using the cold seep mussels Gigantidas childressi, G. mauritanicus, Bathymodiolus heckerae and B. boomerang. We combined COI barcoding of 763 individuals with VIKING20X larval dispersal modelling at a large spatial scale not previously investigated. Population genetics supported the parallel evolution of Gigantidas and Bathymodiolus genera in the Atlantic Ocean and the occurrence of a 1-3 Million-year-old vicariance effect that isolated populations across the Caribbean Sea. Both population genetics and larval dispersal modelling suggested that contemporary gene flow and larval exchanges are possible across the AEB and the Caribbean Sea, although probably rare. When occurring, larval flow was eastward (AEB - only for B. boomerang) or northward (Caribbean Sea - only for G. mauritanicus). Caution is nevertheless required since we focused on only one mitochondrial gene, which may underestimate gene flow if a genetic barrier exists. Non-negligible genetic differentiation occurred between Barbados and African populations, so we could not discount the incomplete lineage sorting hypothesis. Larval dispersal modelling simulations supported the genetic findings along the American coast with high amounts of larval flow between the Gulf of Mexico (GoM) and the US Atlantic Margin, although the Blake Ridge population of B. heckerae appeared genetically differentiated. Overall, our results suggest that additional studies using nuclear genetic markers and population genomics approaches are needed to clarify the evolutionary history of the Atlantic bathymodioline mussels and to distinguish between ongoing and past processes.