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The increasing power/load demand is becoming a new concern for the grid operators as it can potentially overload transmission lines. Among advantages of a multi-terminal dc (MTDC) grid, its high controlability makes it a promising asset for ac line overload alleviation. This paper proposes a model predictive control based strategy, which regularly updates the power setpoints of the MTDC converter stations and ac generators to alleviate ac line overloads. To compute and update the power setpoints, necessary measurements are received by the controller within regular time intervals. The proposed controller ensures that subsequent to any ac line overload, changing the power setpoints of the MTDC converter station does not cause any operation violation in the MTDC grid. Furthermore, it ensures that the ac voltage limits and voltage stability criteria are met to avoid voltage instability. Performance and effectiveness of the proposed controller are evaluated by simulation studies on two systems, i.e., the 39-bus New England system integrated with a 5-bus MTDC system and the IEEE 118-bus system connected to a 6-bus MTDC system. Simulation results confirm that the MTDC grid can play a major role in controlling active powers of most of the ac transmission lines. [ABSTRACT FROM AUTHOR]