| Everyday, we are faced with a lot of uncertainties and discrete decisions. Stochastic mixed integer programming is well suited to help us handle this situation. However, this type of optimization problems are not easy to solve. The first half this dissertation gives a brief review of stochastic programming and stochastic mixed integer programming, and proposes a solution method, embedded Benders' decomposition. Of all these difficult problems, those arising from energy systems are very urgent and important, since in the modern age, instead of human force, people rely more on other energy sources to keep the whole society running. The second half of this dissertation is about stochastic integer optimization applications in energy systems. Firstly, this dissertation studies the stochastic security constrained unit commitment problem, which includes both day-ahead and real time unit commitment, making it a very typical stochastic mixed integer program. Numerical results show that embedded Benders decomposition method suits well this problem, especially when it has a large number of scenarios. Secondly, this dissertation discusses optimization models and algorithms in the natural gas industry, and proposes natural gas transmission system expansion planning models which include both natural gas transmission network expansion and LNG (Liquified Natural Gas) terminals location planning. These models take into account the uncertainties of demands and supplies in the future, which make the models stochastic integer programs with discrete subproblems. In addition, this dissertation considers risk control in these models by including probabilistic constraints, such as a limit on CVaR (Conditional Value at Risk). In order to solve the large-scale problems, especially those with large numbers of scenarios, the embedded Benders decomposition algorithm is applied to tackle the discrete subproblems. Numerical results show that this algorithm is efficient for solving large scale stochastic natural gas transportation system expansion planning problems. |
