This dissertation focuses on computational issues of applying two-stage stochastic programming for long-term and short-term generation planning problems from the perspective of scenario generation and reduction. It follows a three-paper format, in which each paper discusses approaches to generating probabilistic scenarios and then reducing the substantial computational burden caused by a huge number of scenarios for different applications in power systems.
The first paper investigates a long-term generation expansion planning model with uncertain annual load and natural gas price. A two-stage stochastic program is formulated to minimize the total expected expansion cost, generation cost and penalties on unserved energy while satisfying aggregated operational constraints. A statistical property matching technique is applied to simulate plausible future realizations of annual load and natural gas price over the whole planning horizon. To mitigate the computational complexity of a widely used classic scenario reduction method in this context, we firstly cluster scenarios according to the wait-and-see solution for each scenario and then apply the fast forward selection (FFS) method.
The second paper prepares a basis for load scenario generation for the day-ahead reliability unit commitment problem. For the purpose of creating practical load scenarios, epi-splines, based on approximation theory, are employed to approximate the relationship between load and weather forecasts. The epi-spline based short-term load model starts by classifying similar days according to daily forecast temperature as well as monthly and daily load patterns. Parameters of the epi-spline based short-term load model are then estimated by minimizing the fitted errors. The method is tested using day-ahead weather forecast and hourly load data obtained from an Independent System Operator in the U.S. By considering the non-weather dependent load pattern in the short-term load model, the model not only provides accurate load predictions and smaller prediction variances in the validated days, but also preserves similar intraday serial correlations among hourly forecast loads to those from actual load.
The last paper in this dissertation proposes a solution-sensitivity based heuristic scenario reduction method, called forward selection in recourse clusters (FSRC), for a two-stage stochastic day-ahead reliability unit commitment model. FSRC alleviates the computational burden of solving the stochastic program by selecting scenarios based on their cost and reliability impacts. In addition, the variant of pre-categorizing scenarios improves the computational efficiency of FSRC by simplifying the clustering procedure. In a case study down-sampled from an Independent System Operator in the U.S., FSRC is shown to provide reliable commitment strategies and preserve solution quality even when the reduction is substantial
