Stochastic Mixed Integer Problems for Bidding in Sequential Electricity Markets - Scenariowise decomposition approaches

With an increasing number of ancillary services and energy markets, the decision making process for a power producer is becoming more complex. This thesis investigates the bidding problem of a Norwegian hydropower producer bidding in the sequential primary reserve market and day-ahead market. The model implemented is a stochastic mixed integer programming (SMIP) problem with continuous first stage variables and mixed integer second stage variables. SMIP problems are known to be hard to solve and by having continuous first stage variables combined with second stage mixed-integer variables the complexity further increases. This thesis investigates the potential benefits of solving the problem by scenariowise decomposition. A comprehensive case study of the problem is conducted with realistic input data. Stochastic problems are dependent upon a good representation of the uncertainty and realistic price scenarios based on historical price data are therefore created. The results show that scenariowise decomposition of the problem results in better optimistic bounds compared to solving the linear programming relaxation. When the number of scenarios grow, the decomposition methods perform better compared to solving the standard deterministic formulation of the deterministic equivalent. The decomposition methods are however sensitive to the size and complexity of the subproblems, resulting in low scalability with respect to the size of the subproblems. This results in longer solution times than what may be acceptable for a power producer. However, combined with heuristics the methods return bounds which can provide information about the quality of the heuristic solution