Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC's birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.

Power generation expansion planning needs to deal with future uncertainties carefully, given that the invested generation assets will be in operation for a long time. Many stochastic programming models have been proposed to tackle this challenge. However, most previous works assume predetermined future uncertainties (i.e., fixed random outcomes with given probabilities). In several recent studies of generation assets' planning (e.g., thermal versus renewable), new findings show that the investment decisions could affect the future uncertainties as well. To this end, this paper proposes a multistage decision-dependent stochastic optimization model for long-term large-scale generation expansion planning, where large amounts of wind power are involved. In the decision-dependent model, the future uncertainties are not only affecting but also affected by the current decisions. In particular, the probability distribution function is determined by not only input parameters but also decision variables. To deal with the nonlinear constraints in our model, a quasi-exact solution approach is then introduced to reformulate the multistage stochastic investment model to a mixed-integer linear programming model. The wind penetration, investment decisions, and the optimality of the decision-dependent model are evaluated in a series of multistage case studies. The results show that the proposed decision-dependent model provides effective optimization solutions for long-term generation expansion planning.

Wind energy is rapidly growing. While wind brings us clean and inexpensive energy, its inherent variability and uncertainty present challenges for the power grid. In particular, employing wind energy for power system restoration is very challenging. A fast and reliable restoration plays a vital role to achieve the self-healing power grid. This paper develops a novel offline restoration planning tool for harnessing wind energy to enhance grid resilience. The wind-for-restoration problem is formulated as a stochastic mixed-integer linear programming problem with generated wind energy scenarios. The problem is then decomposed into two stages and solved with the integer L-shaped algorithm. Numerical experiments have been conducted through different case studies using the modified IEEE 57-bus system. The developed tool can provide the scheduled wind power at each restoration time. The impact of wind energy is investigated from the aspects of location and inertia capability, as well as wind penetration, fluctuation, and uncertainty. Moreover, a dynamic response validation tool is developed to validate the results of optimization problem in a dynamic simulation software. Simulation results demonstrate that the optimal wind harnessing strategy can help improve system restoration process and enhance system resilience.