Design and optimization under uncertainty of Energy Systems

In many engineering design and optimisation problems, the presence of uncertainty in data and parameters is a central and critical issue. The analysis and design of advanced complex energy systems is generally performed starting from a single operating condition and assuming a series of design and operating parameters as fixed values. However, many of the variables on which the design is based are subject to uncertainty because they are not determinable with an adequate precision and they can affect both performance and cost. Uncertainties stem naturally from our limitations in measurements, predictions and manufacturing, and we can say that any system used in engineering is subject to some degree of uncertainty. Different fields of engineering use different ways to describe this uncertainty and adopt a variety of techniques to approach the problem. The past decade has seen a significant growth of research and development in uncertainty quantification methods to analyse the propagation of uncertain inputs through the systems. One of the main challenges in this field are identifying sources of uncertainty that potentially affect the outcomes and the efficiency in propagating these uncertainties from the sources to the quantities of interest, especially when there are many sources of uncertainties. Hence, the level of rigor in uncertainty analysis depends on the quality of uncertainty quantification method. The main obstacle of this analysis is often the computational effort, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation through a non-intrusive approach with as few evaluations as possible. The primary goal of this work is to show a robust method for uncertainty quantification applied to energy systems. The first step in this direction was made doing a work on the analysis of uncertainties on a recuperator for micro gas turbines, making use of the Monte Carlo and Response Sensitivity Analysis methodologies to perform this study. However, when considering more complex energy systems, one of the main weaknesses of uncertainty quantification methods arises: the extremely high computational effort needed. For this reason, the application of a so-called metamodel was found necessary and useful. This approach was applied to perform a complete analysis under uncertainty of a solid oxide fuel cell hybrid system, starting from the evaluation of the impact of several uncertainties on the system up to a robust design including a multi-objective optimization. The response surfaces have allowed the authors to consider the uncertainties in the system when performing an acceptable number of simulations. These response were then used to perform a Monte Carlo simulation to evaluate the impact of the uncertainties on the monitored outputs, giving an insight on the spread of the resulting probability density functions and so on the outputs which should be considered more carefully during the design phase. Finally, the analysis of a complex combined cycle with a flue gas condesing heat pump subject to market uncertainties was performed. To consider the uncertainties in the electrical price, which would impact directly the revenues of the system, a statistical study on the behaviour of such price along the years was performed. From the data obtained it was possible to create a probability density function for each hour of the day which would represent its behaviour, and then those distributions were used to analyze the variability of the system in terms of revenues and emissions.