Nowadays renewable energy sources (RES) are growing at a rapid pace, particularly the wind energy. The high amount of wind power penetration into the power grids poses a major challenge to Transmission System Operators (TSO) in terms of the operational management, as wind power is highly uncertain. The highly uncertain nature of the wind power leads to the scenarios where the power flow exceeds the grid limits leading to the capacity problem of the grid. There are multiple solutions to prevent this grid capacity problem. The first solution is the physical extension of the grid, but this requires considerable capital investments. Moreover, the frequency of the worst-case scenarios (maximum generation coinciding with minimum load) is very low and grid expansion is a much slower process, so this solution is not optimal. The second solution is to store the excessive power using batteries. The batteries cannot store power efficiently because of the storage losses and they also degrade with time. The initial setup of the batteries and their replacement (in the case of degradation) would require considerable capital investments. The third solution is reserve regulation of the generation units to deal with the uncertainty of wind power. The final solutions is to curtail excessive wind power in the grid. The last two solutions are feasible from an economic point of view when compared to the initial two solutions. However, both these approaches are expensive. But, an optimal combination of these approaches might result in an enhanced solution in terms of total energy procurement costs (a cheaper solution).

The objective of this thesis is to formulate a chance-constrained multivariate stochastic optimization problem which would perform the stochastic unit commitment and simultaneously would create an optimal combination of wind power curtailment and reserve scheduling to reduce the overall costs of the system. As an initial step, the combination of the reserves and wind power curtailment (the convex combination approach) was modeled using the convex combination approach. The optimization problem corresponding to the convex combination model was formulated to find an optimal combination of reserve dispatch and wind power curtailment. Later on, the combination of reserve scheduling and the wind power curtailment was modeled using the mixed logic dynamical systems framework (MLD approach). The optimization problem corresponding to the MLD approach was formulated to find an optimal combination of reserve dispatch and wind power curtailment.

A randomization technique was used to generate various scenarios of the uncertain wind power. Based on a prior violation level of the grid limits, we perform scenario-based stochastic optimization to obtain an optimal combination of reserve scheduling and wind power curtailment in both the approaches for each scenario to lower the overall costs of the system. The theoretical developments proposed were evaluated on an IEEE-30 bus network.
The static and the dynamic demand cases were simulated. In both cases, the proposed approaches outperformed the reserve scheduling method.