Temporal resolution in energy systems optimization models
Keywords: Energy Resources Engineering.

The electricity sector will play an important role in the transition to a more sustainable energy system. In order to reduce the sector's carbon dioxide emissions, renewable energy is becoming more and more significant. Because renewable energy is time-varying and non-dispatchable, it requires high temporal modeling resolution. However, energy system optimization studies, which are used for the planning of future energy systems, are often computationally intractable when modeled with high temporal resolution. We develop and use time-series aggregation (TSA) methods, which reduce temporal model complexity, to address this challenge. Different TSA methods have emerged for a multitude of energy applications in different fields. In Chapter 2, we review the literature and provide both an introduction for researchers using TSA for the first time and a guide to "connect the dots" for experienced researchers in the field. We show where time series affect optimization models, and define the goals, inherent assumptions, and challenges of TSA. We review the methods that have been proposed in the literature, focusing on how these methods address the challenges. We recommend the following best practices when using TSA: (1) performance should be measured in terms of optimization outcome and should be validated on the full time series; (2) TSA methods and optimization problem formulation should be tuned for the specific problem and data; (3) wind data should be aggregated with extra care; (4) bounding the error in the objective function should be considered. Clustering is the most commonly used TSA method for energy systems optimization problems. In Chapter 3, we introduce a framework and systematically investigate clustering methods used for this purpose. We compare both conventionally used methods (k-means, k-medoids, and hierarchical clustering), as well as shape-based clustering methods (dynamic time warping barycenter averaging and k-shape). We compare these methods in the domain of the objective function of two example operational optimization problems: battery charge/discharge optimization and gas turbine scheduling, both of which exhibit characteristics of more complex optimization problems. We show that centroid-based clustering methods represent the operational part of the optimization problem more predictably than medoid-based approaches but result in biased objective function estimates. On certain problems that exploit intra-day variability, such as battery scheduling, we show that k-shape improves performance significantly over conventionally-used clustering methods. Comparing all locally-converged solutions of the clustering methods, we show that a better representation in terms of clustering measure is not necessarily better in terms of objective function value of the optimization problem. In general, clustering removes extreme events from the data. These extreme events can be important to achieve reliable system designs. In Chapter 4, we present a framework and a method to include extreme periods into TSA. Our method is applied to Generation Capacity Expansion Planning, which determines a set of investments to optimally supply future electricity demand. Our proposed method guarantees reliable system designs on the full input data even though only the reduced data set is used for system design. Our method iteratively adds extreme periods to the set of representative periods based on information from the optimization problem itself until lost load is zero. We perform a comprehensive analysis on several case studies of both German and Californian energy systems and show that our method leads to meeting electricity demand at all times, reducing lost load by 1.9%-16.3%. We show that our method outperforms the state-of-the-art method of adding a pre-defined number of extreme periods based on statistical properties of the data itself. When planning for the energy system of the future, the challenge is that time-varying input data are highly uncertain, both in terms of their magnitude and the shape of their profile. In Chapter 5, we explore whether including electricity price uncertainty into the design process of electricity-intensive electrochemical processes affects design decisions, and whether it can lead to better investment decision making. We apply stochastic optimization to the design and operations of a chlor-alkali plant, which produces chlorine, caustic soda, and hydrogen using electricity. The process is electricity intensive and can be operated flexibly based on fluctuating electricity prices. We consider participation in the 5-minute real time market and consider each day as a scenario in the stochastic program, where we optimize for net present value of profits. We find that flexible plant designs that oversize certain plant components can enhance participation in electricity markets and increase profits. We also find that including future electricity price uncertainty in system design optimization of the chlor-alkali process leads to improved design decision making. When uncertainty is considered by using a stochastic optimization formulation, the optimal system design includes fuel cell capacity and hydrogen storage capacity, which allow the plant to hedge against price uncertainty. In an analogy to TSA in deterministic optimization problems, we furthermore investigate the effect of scenario reduction techniques in this stochastic optimization problem, and whether scenario reduction techniques retain information about uncertainty. We find that for our example problem, scenario reduction approximates expected objective function value well, but leads to error in terms of optimal design decision variables