Hydropower Aggregation by Spatial Decomposition – an SDDP Approach

The balance between detailed technical description, representation of uncertainty and computational complexity is central in long-term scheduling models applied to hydro-dominated power system. The aggregation of complex hydropower systems into equivalent energy representations (EER) is a commonly used technique to reduce dimensionality and computation time in scheduling models. This work presents a method for coordinating the EERs with their detailed hydropower system representation within a model based on stochastic dual dynamic programming (SDDP). SDDP is applied to an EER representation of the hydropower system, where feasibility cuts derived from optimization of the detailed hydropower are used to constrain the flexibility of the EERs. These cuts can be computed either before or during the execution of the SDDP algorithm and allow system details to be captured within the SDDP strategies without compromising the convergence rate and state-space dimensionality. Results in terms of computational performance and system operation are reported from a test system comprising realistic hydropower watercourses.Hydropower Aggregation by Spatial Decomposition – an SDDP ApproachacceptedVersio

Robust Low-Cost Multiple Antenna Processing for V2V Communication

Cooperative V2V communication with frequent, periodic broadcast of messages between vehicles is a key enabler of applications that increase traffic safety and traffic efficiency on roads. Such broadcast V2V communication requires an antenna system with omnidirectional coverage, which is difficult to achieve using a single antenna element. For a mounted, omnidirectional antenna on a vehicle is distorted by the vehicle body, and exhibits a nonuniform directional pattern with low gain in certain directions. The thesis addresses this problem by developing schemes that employ multiple antennas (MAs) to achieve an effective radiation pattern with omnidirectional characteristics at both the transmit- and the receive-side. To ensure robust communication, the MA schemes are designed to minimize the burst error probability of several consecutive status messages in a scarce multipath environment with a dominant path between vehicles.First, at the receive-side, we develop a hybrid analog-digital antenna combiner. The analog part of the combiner is composed of low-cost analog combining networks (ACNs) of phase shifters that do not depend on channel stateinformation (CSI), while the digital part uses maximal ratio combining. We show that the optimal phase slopes of the analog part of the combiner (i.e., the phase slopes that minimize the burst error probability) are the same found under the optimization of a single ACN, which was done in earlier work. We then show how directional antennas can be employed in this context to achieve an effective omnidirectional radiation pattern of the antenna system that is robust in all directions of arrival of received signals.Secondly, at the transmit-side, we develop two low-cost analog MA schemes, an analog beamforming network (ABN) of phase shifters, and an antenna switching network (ASN), for the case when receivers employ the ACN or the hybrid combiner. Both schemes are shown to achieve an effective radiation pattern with improved omnidirectional characteristics at the transmit-side without relying on CSI.Thirdly, the schemes above were developed assuming that all vehicles broadcast their messages with the same fixed period. Therefore, we tackle the practical scenario when different vehicles use different and potentially varying broadcast periods. We show that the phase slopes of the MA schemes at the receiver and/or transmitter can be designed to support multiple broadcast periods.\ua0Lastly, the optimal phase slopes of the MA schemes were analytically derived under a worst-case propagation corresponding to a dominant path with an angle of departure, and an angle of arrival that are approximately non-varying over the time it takes to transmit and receive several packets. We relax this assumption and study the system performance under a time-varying dominant component instead. We derive a design rule that yields robust phase slopes that effectively mitigate the losses due to the time-variation of the dominant path

Robust multiple stopping -- A path-wise duality approach

In this paper we develop a solution method for general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model uncertainty, and for general reward processes driven by multi-dimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem which satisfy appealing path-wise optimality (almost sure) properties. Next, we exploit these theoretical results to develop upper and lower bounds which, as we formally show, not only converge to the true solution asymptotically, but also constitute genuine upper and lower bounds. We illustrate the applicability of our general approach in a few examples and analyze the impact of model uncertainty on optimal multiple stopping strategies

A Planner-Trader Decomposition for Multi-Market Hydro Scheduling

Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bi-layer stochastic programming framework for the optimal operation of a fleet of interconnected hydropower plants that sells energy on both the spot and the reserve markets. The outer layer (the planner's problem) optimizes end-of-day reservoir filling levels over one year, whereas the inner layer (the trader's problem) selects optimal hourly market bids within each day. Using an information restriction whereby the planner prescribes the end-of-day reservoir targets one day in advance, we prove that the trader's problem simplifies from an infinite-dimensional stochastic program with 25 stages to a finite two-stage stochastic program with only two scenarios. Substituting this reformulation back into the outer layer and approximating the reservoir targets by affine decision rules allows us to simplify the planner's problem from an infinite-dimensional stochastic program with 365 stages to a two-stage stochastic program that can conveniently be solved via the sample average approximation. Numerical experiments based on a cascade in the Salzburg region of Austria demonstrate the effectiveness of the suggested framework

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization