Advanced mathematical modeling related to comprehensive energy system models

Abstract

In the strive of analyzing possible pathways towards low-carbon economies a new paradigm of energy system models have arisen. To reach the 1.5 C climate ambitions, fossil fuels are replaced by Variable Renewable Energies (VRE) creating the need for efficient modeling of system flexibility. Optimal levels of flexible capacities are identified by simultaneously optimizing long-term capacity expansion decisions and short-term operational decisions. New energy models therefore not only have to optimize a broader sector-coupled system e.g. the coupling of electricity and gas but also have to consider a significantly more detailed time resolution. The transformation of such comprehensive energy systems into mathematical optimization models frequently leads to high computational complexities. The new paradigm of energy system models therefore calls for more efficient solution procedures. An increasingly popular approach to regain tractability is to strategically reduce the time domain. In that sense, time aggregation approaches aim at gaining a significant reduction in problem size with limited decrease in solution quality. Aggregation approaches have especially gained increased attention within the research field of Capacity Expansion Planning (CEP) where numerous aggregation techniques have been developed to tame the high complexity. Nevertheless, the increased shares of VRE challenge the existing approaches in properly capturing the variability in the supply side. In addition, the developed methods are frequently not properly validated which causes two major research questions to arise: First, how good solutions one can expect from aggregated problems and second what essential properties of aggregation techniques that may maximize the quality of the aggregated problem solutions. To study these question, this thesis provides methodologies to strategically validate and compare different time aggregation techniques within a broad spectrum of possible energy system challenges. New aggregation techniques are developed aiming at more efficiently capturing the increased level of variability in the supply side. With various case studies we not only illustrate the value of the time aggregation tool to the current and future energy system models, but also identify key properties of aggregation techniques which constitute a foundation for the further development of aggregation techniques. This thesis further contributes to the literature by proposing efficient solution procedures that exploits the high quality of aggregated solutions. Math-heuristics are developed which search the neighborhood around the investment decisions obtained from an aggregated problem with the goal of closing the optimality gap. This approach therefore act as a quality guarantee that may account for what the aggregated problem is not capable of capturing. Lastly, opposed to finding a single optimal solution we argue that a portfolio of diverse near optimal solutions may provide a much better understanding of the problem. Following this idea, we suggest a framework that explores the near optimal solution space by iteratively finding new solutions which are as different as possible from earlier solutions with respect to investment decisions. In conclusion, this thesis contributes with new and improved methods to efficiently solve the new paradigm of energy system models. Even though the methodologies are developed in the framework of CEPs, the different approaches are highly general and may be applied to other time dependent investment problems.