The present PhD thesis deals with transformer inrush current in offshore grids including offshore wind farms and High Voltage Direct Current (HVDC) transmission systems. The inrush phenomenon during transformers energization or recovery after the fault clearance is one of important concerns in offshore systems which can threaten the security and reliability of the HVDC grid operation as well as the wind farms function. Hence, the behaviour of wind turbines,Voltage Source Converters (VSC) and transformer under the normal operation and the inrush transient mode is analyzed. For inrush current reduction in the procedure of the offshore wind farms start-up and integration into the onshore AC grid, a technique based on Voltage Ramping Strategy (VRS) is proposed and its performance is compared with the operation of system without consideration of this approach. The new methodology which is simple, cost-effective ensures minimization of transformer inrush current in the offshore systems and the enhancement of power quality and the reliability of grid under the transformer energizing condition. The mentioned method can develop much lower inrush currents according to the slower voltage ramp slopes. Concerning the recovery inrush current, the operation of the offshore grid especially transformers is analyzed under the fault and the system restoration modes.The recovery inrush transient of transformers can cause tripping the HVDC and wind farms converters as well as disturbing the HVDC power transmission. A voltage control design based on VRS is proposed in HVDC converter to recover ali the transformers in offshore grid with lower inrush currents.The control system proposed can assure the correct performance of the converters in HVDC system and in wind farm and also the robust stability of the offshore grid. Esta tesis doctoral estudia las corrientes de energización de transformadores de parques eólicos marinos con aerogeneradores con convertidores en fuente de tensión (VSC) de plena potencia conectados a través de una conexión de Alta Tensión en Corriente Continua (HVDC). Las corrientes de energización pueden disminuir la fiabilidad de la transmisión eléctrica debido a disparos intempestivos de las protecciones durante la puesta en marcha o recuperación de una falta. Para la mitigación de las corrientes de energización durante la puesta en marcha del parque esta tesis propone una nueva estrategia basada en incrementar la tensión aplicada por el convertidor del parque eólico en forma de rampa (VRS). Este método persigue energizar el parque eólico con el menor coste y máxima fiabilidad. La tesis analiza diferentes escenarios y diferentes rampas. Otro momento en que las corrientes de energización pueden dar lugar a un disparo intempestivo de las protecciones es durante la recuperación de una falta en la red de alterna del parque eólico marino. Esta tesis extiende la estrategia VRS, utilizada durante la puesta en marcha del convertidor del parque, para los escenarios de recuperación de una falta.