Power systems nowadays are experiencing a significant energy transition characterized by the progressive increment of power electronic interfaced units. Voltage source converters are extensively utilized to interconnect renewable energy sources at various transmission levels, facilitate the asynchronous interconnection of system areas through HVDC links and enable the installment of responsive demand units into the grid. The latter increase of power electronic interfaced units in the power system has significantly altered its dynamic behavior as the system is characterized by low inertia conditions, fast and more frequent dynamics, lack of inertial response, limited short circuit capability and uncertain generation and demand mixes. Under these new operating conditions one of the main concerns of TSOs is the ability of the system to withstand active power-frequency imbalances. To cope with the frequency stability issues encountered, power electronic interfaced elements introduced, can be effectively utilized to offer ancillary services such as fast frequency support to the grid due to the high controllability levels and the rapid response capability they exhibit. This thesis project deals with the optimization of the frequency response of a multi-area, multi-energy hybrid HVAC-HVDC power system when common active power-frequency disturbances occur. The system analyzed consists of 3 electromagnetically decoupled areas through MMC-HVDC interconnection links with different generation and demand mixes characterized by different inertia levels due to the integration of fully decoupled wind turbines type IV and proton exchange membrane electrolyzers. The controllers of the power electronic interfaced elements have been modified with the active power gradient control scheme to provide fast frequency support in case of commonly occurred active power-frequency imbalances. However, to avoid insufficient or over regulation of the systems’ frequency when multiple elements target the same variable, a coordinated tuning strategy is more than necessary. For this reason, in this study two different problem formulations have been proposed aiming at a coordinated tuning of the parameters of the frequency controllers of the synthetic inertia elements participating in the frequency regulation. To effectively solve the optimization problem and enhance the frequency stability of the system a powerful metaheuristic optimization algorithm, the mean variance mapping optimization algorithm has been used. The optimization results can effectively highlight the tuning strategy that achieves the best frequency response of the system under various commonly occurred active power-frequency disturbances and provide further insight on the proper utilization of various synthetic inertia sources with respect to their response capabilities and location.