Power systems worldwide are embracing diverse supply mixes that incorporate a significant portion from renewables such as wind and solar energy. Wind energy is characterised by reliable equipment, but with an output that is uncertain and intermittent. In addition to equipment unreliability (system N-1 criterion), output uncertainties of wind electric generators (WEGs) introduce risk into daily power system schedules. This risk from the uncertainty of output from WEGs can be quantified as expected energy not served (EENS). Furthermore, the introduction of new forms of generation changes the methods of operating transmission systems, further necessitating the use of transmission security constraints in power systems optimization algorithms. This dissertation explores new approaches to stochastically model the real power output of WEGs and to efficiently tackle AC transmission system security constraints for power system optimization algorithms such as optimal power flow (OPF) and day-ahead unit commitment (UC). Usually, normal probabilistic distribution is used to model uncertainty in short-term wind power output forecast and compute EENS. In this dissertation, a new triangular approximate distribution (TAD) model is proposed which is a linear approximation of normal probabilistic distribution to model short-term wind power output forecast and compute EENS. This TAD model is used to formulate a practical risk-constrained fast OPF for transmission systems to simultaneously minimize: 1) risk due to uncertainties in power output from WEGs, and 2) the total operating cost. The integration of new energy resources causes transmission systems to operate in new, challenging, and often unforeseen operating states. Thus, it is imperative that UC algorithms incorporate AC transmission system security constraints and stochastically model output of WEGs to ensure reliable operation of transmission systems. As a first step, a successive mixed integer linear programming (MILP) method is proposed for AC transmission system security constrained unit commitment (SCUC) challenge. Fuzzy sets theory is used to model infeasible constraints in this MILP formulation. As a next step, the TAD model of WEGs is integrated into the MILP formulation of SCUC to create a fast security and risk constrained probabilistic UC algorithm. The two UC algorithms are tested on large systems.