The resilience of future power systems are being challenged in three fronts: (i) decarbonising energy supply will alter supply mix; (ii) shift of previous non-electric demand onto the energy network will require the system to work at higher capacity; and (iii) expected changes in climate will alter demand and performance of electrical network components. This thesis quantitatively assesses the impact of future climate change on the resilience of a power system, in secure and hazardous conditions. This is done through the use of reliability indices and probabilistic security assessment. Dynamical thermal ratings of circuits are used throughout this thesis given their potential for increased capacity over the standard static ratings. The first finding is that the predicted future climate scenarios will result in components with lower thermal ratings then if used currently. Due to this, it is found that the reliability of the system decreases under further climate scenarios. In order to keep a satisfactory level of reliability in the system, a method of temporary overloaded circuits is introduced which doesn't result in a higher risk of component failure. The temporary overload method allows for the rating constraint to be violated provided the temperature constraint isn't. Applying this to the system, and assessing the results under various climate scenarios, it is found that the method is beneficial in terms of economical cost and system reliability. When applied to hazardous conditions, it is found the method has a higher potential to strengthen the reliability of the system in comparison to when used on the 'safe' system.An approach is taken to aid the system operator in decision making under uncertain conditions. A scenario is devised in which an operator wants to plan the power dispatch for a future time period. This is done through the use of stochastic optimisation, where the uncertainty is encapsulated by the conductor ratings which are calculated using dynamical thermal ratings in which the weather parameters are stochastic. This is developed for a one and two period model, in which the two period model has the first and second period coupled through the addition of a ramp rate constraint in the optimisation. System adequacy indices and probabilistic security indices are added as constraints so the system operator can control the reliability of his system.