The preferred technology for connecting far from shore offshore wind plants to the onshore AC power system is the voltage-source converter based high voltage direct current (VSC-HVDC) transmission system. There is a large number of advantages, namely, the decoupled active and reactive power control, the capability to reverse power flows without changing voltage polarity and finally, the capability to operate in weak and isolated power systems. Beside the above mentioned advantages, HVDC systems are capable to transport large amounts of power within large distances. The minimal cable power loss makes it desirable to use HVDC technologies in order to transport electrical power for distances above 60 km. Future power systems are expected to include large in-feed of power electronic based generation as a result of converter interfaced renewable energy resources. Furthermore, the construction of a Pan-European HVDC transmission network, mainly used as bulk transmission system, will enable the inter-connection of previously asynchronous systems in a multi-terminal DC grid. Furthermore, it will enable large offshore wind power plants to be part of this MTDC grid. However, even if it seems that the onshore AC power systems are inter-connected in a MTDC grid, the HVDC converters forming part of the MTDC network will decouple the AC power system dynamics. Having the networks decoupled, in case of disturbances such as faults, tripping of generation unit, puts the system’s frequency stability into greater risk. The present thesis deals with the study of different methods of providing primary frequency response by making use of the multi-terminal direct current (MTDC) network. The AC systems’ primary frequency response is investigated, and controllers for provision of primary response are proposed. To this purpose, two configurations have been studied, a point-to-point and a multi-terminal topology. In both situations an offshore wind park is connected, through VSC-HVDC transmission, to one or more onshore AC power systems, modelled by single machine dynamic model. The time-average, instantaneous value modelling approach is used for the VSC-HVDC system; it contains control systems, phase-locked loop and detailed representation of DC transmission lines. The controllers proposed for the primary frequency response study are: a frequency droop controller which provides primary frequency response, a synthetic inertia emulation controller implemented on the DC voltage control loop of the HVDC converter and finally, a synthetic inertia controller using the frequency derivative, directly measured at the grid connection point. Since the power injection by a voltage-source converter can be controlled, the above mentioned controllers can be used to assist the frequency response of the AC power systems. Following a disturbance (i.e. trip of a unit), the frequency droop control method utilizes the deviation in system frequency from the nominal value, to adjust the power being supplied to the AC area. The synthetic inertia emulation controller employs the energy stored in the capacitors to emulate inertia response by changing the DC link voltage reference, based on the variation of the AC system’s frequency. In a MTDC scheme, such a method can be used to provide exchange of primary frequency reserves between asynchronous areas. The last control method uses the frequency derivative to control the active power in the converters, to strengthen the primary frequency response of the AC system undergoing a disturbance. Finally, sensitivity analysis of the above control parameters is performed to investigate various interactions between the AC and the DC system.