Distributed or multi-area optimal power flow (OPF) in alternating current (AC) grids is currently a subject undergoing intense study to cope with computational burdens in large-scale grids and to maintain self-control of a regional system operator. However, future power grids will most likely be hybrid grids consisting of the conventional AC transmission system combined with high voltage direct current (DC) technology. Thus, we reformulate the full AC-DC OPF problem such that it becomes separable and, therefore, accessible to distributed algorithms. Then, we show in detail two different approaches on the decomposition of a hybrid AC-DC grid. Finally, we implement an improved alternating direction of multipliers method (ADMM) as well as the most recently proposed augmented Lagrangian based alternating direction inexact Newton (ALADIN) method. Simulation results show that optimality gaps below 0.01% are reached with both decomposition approaches and algorithms for two different test systems (5-bus and 66-bus). Furthermore, convergence rates and wall clock times are reduced by around one order of magnitude from ADMM to ALADIN.Index Terms-Distributed optimal power flow, multi-area optimal power flow, AC-DC grid, ADMM, ALADIN.

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