We consider a hydrothermal scheduling problem with a mid-term horizon(HTSPM) modeled as a large-scale multistage stochastic program with stochastic monthly inflows of water to each hydro generator. In the HTSPM we seek an operating policy to minimize the sum of present and expected future costs, which include thermal generation costs and load curtailment costs. In addition to various simple bounds, problem constraints involve water balance, demand satisfaction and power interchanges. Sampling-based decomposition algorithms (SBDAs) have been used in the literature to solve HTSPM. SBDAs can be used to approximately solve problem instances with many time stages and with inflows that exhibit interstage dependence. Such dependence requires care in computing valid cuts for the decomposition algorithm. In order to help maintain tractability, we employ an aggregate reservoir representation (ARR). In an ARR all the hydro generators inside a specific region are grouped to effectively form one hydro plant with reservoir storage and generation capacity proportional to the parameters of the hydro plants used to form that aggregate reservoir. The ARR has been used in the literature with energy balance constraints, rather than water balance constraints, coupled with time series forecasts of energy inflows. Instead, we prefer as a model primitive to have the time series model forecast water inflows. This, in turn, requires that we extend existing methods to compute valid cuts for the decomposition method under the resulting form of interstage dependence. We form a sample average approximation of the original problem and then solve this problem by these special-purpose algorithms. And, we assess the quality of the resulting policy for operating the system. In our analysis, we compute a confidence interval on the optimality gap of a policy generated by solving an approximation on a sampled scenario tree. We present computational results on test problems with 24 monthly stages in which the inter-stage dependency of hydro inflows is modeled using a dynamic linear model. We further develop a parallel implementation of an SBDA. We apply SBDA to solve the HTSPM for the Brazilian power system that has 150 hydro generators, 151 thermal generators and 4 regions that each characterize an aggregate reservoir. We create and solve four different HTSPM instances where we change the input parameters with respect to generation capacity, transmission capacity and load in order to analyze the difference in the total expected cost. / text

In a hydro-dominated system, such as New Zealand, the continual improvement and development of effective optimization and simulation software to inform decision making is necessary for effective resource management. Stochastic Constructive Dual Dynamic Programming (SCDDP) is a technique which has been effectively applied to the New Zealand system for optimization and simulation. This variant of Dynamic Programming (DP) allows optimization to occur in the dual space reducing the computational complexity and allows solutions from a single run to be formed as price signal surfaces and trajectories. However, any application of this method suffers from issues with computational tractability for higher reservoir numbers. Furthermore, New Zealand specific applications currently provide limited information on the system as they all use the same two-reservoir approximation of the New Zealand system. This limitation is of increasing importance with the decentralization of the New Zealand electricity sector. In this thesis we develop this theory with respect to two key goals: • To advance the theory surrounding SCDDP to be generalizable to higher reservoir numbers through the application of the point-wise algorithm explored in R. A. Read, Dye, S. & Read, E.G. (2012) to the stochastic case. • To develop at least two new and distinct two-reservoir SCDDP representations of the New Zealand system to provide a theoretical basis for greater flexibility in simulation and optimization of hydro-thermal scheduling in the New Zealand context.