Power systems conventionally have been designed and operated to facilitate electrical energy transportation from large centralised power plants to distant load centres. It is currently under development towards the purpose of being able to facilitate more distributed generation from renewable energy sources (RES), for instance wind and solar energy. Increasing the share of RES would allow us to replace carbon-intensive energy sources and achieve significant reduction of the greenhouse gas emissions, establish vast and inexhaustible energy supply, and offer more affordable electricity price amongst others. On the other hand, the integration of RES to the existing power systems brings additional challenges to system planners and operators. Transmission system operators (TSOs) are already facing operational challenges of high power flows starting in the areas with large wind power installations in Germany to the remote load centres, observing substantial loop flows through Poland and the Czech Republic. As a consequence, the daily operation of Europe's electricity system is increasingly threatened by the risks of blackouts or component failures with wide-reaching impact. According to ENTSO-E the changing generation mix will contribute to upcoming congestion situations, resulting in a limitation in possible exports. The Commission's Priority Interconnection Plan also points out the danger arising from the operation of networks closer to their physical limits. It is of utmost importance to develop a methodology that is able to identify transmission network bottlenecks, i.e. those components with a high potential to be the origin of a major blackout or cascading event, meanwhile incorporating the uncertainties caused by the RES integration as well as the diversified energy policies in terms of future generation mixes. The improvement of the transmission and distribution infrastructure begins with the identication of its current shortcomings. Another aspect of power system assessment is to investigate transmission congestions, which is labelled as the 'symptom' of the insufficient transfer capacity when the existing capacity cannot facilitate the desired electricity demand. The reduction of congestions is an indicator of social and economic welfare assuming equitable distribution of benefits under the goal of the European Union to develop an integrated market as stated in the ENTSO-E Ten Year Development Plan. A relative small number of additional capacity could lead to major economic benefits for many consumers, as advised by US Department of Energy. For such demanding requests on the power system assessment, there is strong need to translate the explained challenges into an engineering problem, which requires a clear technical vision of the aforementioned challenges in the power system operation and planning, in addition to a clear understanding of power system modelling with substantial supporting material of mathematics. To substantiate the knowledge of both engineering and mathematics, the thesis provides a structured way of elaborating the engineering background of power systems as well as the mathematical formulations that are essential for understanding the novelty of the proposed methods (Chapters 2, 3 and 4 of this thesis). Chapter 5 provides a method for the transmission network assessment taking into account the wind stochasticity using a unified Monte-Carlo method and Copula approach. Two main reasons of using the Monte-Carlo method are a) the anti-aliasing property and b) the ability to quickly approximate the answer that otherwise would be very computation-intensive. The methodology is firstly elaborated and applied to a single scenario study, and further enhanced to a more general approach that allows taking into account multiple scenarios caused by uncertainties raised from energy policy perspectives. The solution set of the multiple scenario study captures the impact of uncertainties of all energy policy perspectives without increasing the size of stochastic infeed inputs. A new method for the transmission expansion planning problem is presented in Chapter 6 and 7, which separate the topic into snapshot-based and multi-stage expansion planning methods. Actively optimising Lagrangian multipliers as 'primal' variables in the optimization problem is used as a tool for the network expansion, providing the copper-plate topology from either a congested or an infeasible grid configuration. The method also emphasizes the over-investment issues by introducing a maximum allowable overloading factor, to prevent a large amount of inefficient investment on 'minor' congestions. The multi-stage expansion planning method further strengthens the snapshot-based method by proposing the optimal network topology at different time horizon chronologically, taking into account the possible scenarios of conventional generation mix, load and wind energy infeed at each stage. The modular approach of functionally partitioning the multi-stage planning methodology offers additional advantages including a) reducing computational effort, b) allowing easy modification of the existing modules, and c) allowing adaptation of other modules for enhancement, etc. The final optimal expansion plan at each stages guarantees the copper-plate network structure subject to various scenarios and wind generation infeeds at the lowest operational and investment costs.