A. James Clark School of Engineering
Permanent URI for this communityhttp://hdl.handle.net/1903/1654
The collections in this community comprise faculty research works, as well as graduate theses and dissertations.
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Item OPTIMAL SCHEDULING OF RESIDENTIAL DEMAND RESPONSE USING DYNAMIC PROGRAMMING(2019) Moglen, Rachel Lee; Gabriel, Steven A; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Electricity price volatility in the Electricity Reliability Council of Texas (ERCOT) poses significant financial threat to many players in the electricity market, though most of the financial burden falls on the retail electric providers (REPs). REPs are contractually obligated to purchase and provide all electricity that the end-user wishes to consume, even when the purchase of this electricity brings them financial losses. Electricity prices in ERCOT can increase from typical ranges ($30/MWh) to $3,000/MWh in as little as 15 minutes, causing REPs to seek mitigation techniques to avoid paying price spike prices for electricity. We explore two techniques for REPs to schedule mitigation techniques: a price prediction-based heuristic approach, as well as an optimal scheduling algorithm using dynamic programming (DP). We aim to optimally schedule these mitigation techniques which shift load from high price periods to times of lower prices, called demand response (DR). To achieve this load shifting, REPs remotely manipulate internet-connected thermostats of residential customers, thereby controlling a fraction of residential HVAC load. We found that the price prediction approach was highly unreliable, even for predicting prices as near as 5 minutes out. We therefore chose to rely on the DP as the primary scheduling model. By applying the DP deterministically to historical electricity price and weather data, the load-shifting technique is shown to potentially improve REP profit margins by 10% to 25% per customer annually. Most of these savings come from a few crucial events, highlighting the usefulness of the DP and the importance of accuracy in the timing of DR events. Due to the uncertainty in electricity prices, we apply a multi-objective approach considering the REP’s conflicting objectives: maximizing savings and minimizing financial risk. Results from this multi-objective formulation point to shorter duration DR events in the evening being the least risky, with additional savings possible through riskier short midday events. To ensure that REPs could apply our DP formulation for use in near real-time decision-making applications, the computation speed was verified to be under one second for 24 stages (i.e., 1-hour intervals for one day.)Item Stochastic Systems with Cumulative Prospect Theory(2013) Lin, Kun; Marcus, Steven I.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Stochastic control problems arise in many fields. Traditionally, the most widely used class of performance criteria in stochastic control problems is risk-neutral. More recent attempts at introducing risk-sensitivity into stochastic control problems include the application of utility functions. The decision theory community has long debated the merits of using expected utility for modeling human behaviors, as exemplified by the Allais paradox. Substantiated by strong experimental evidence, Cumulative Prospect Theory (CPT) based performance measures have been proposed as alternatives to expected utility based performance measures for evaluating human-centric systems. Our goal is to study stochastic control problems using performance measures derived from the cumulative prospect theory. The first part of this thesis solves the problem of evaluating Markov decision processes (MDPs) using CPT-based performance measures. A well-known method of solving MDPs is dynamic programming, which has traditionally been applied with an expected utility criterion. When the performance measure is CPT-inspired, several complications arise. Firstly, when solving a problem via dynamic programming, it is important that the performance criterion has a recursive structure, which is not true for all CPT-based criteria. Secondly, we need to prove the traditional optimality criteria for the updated problems (i.e., MDPs with CPT-based performance criteria). The theorems stated in this part of the thesis answer the question: what are the conditions required on a CPT-inspired criterion such that the corresponding MDP is solvable via dynamic programming? The second part of this thesis deals with stochastic global optimization problems. Using ideas from the cumulative prospect theory, we are able to introduce a novel model-based randomized optimization algorithm: Cumulative Weighting Optimization (CWO). The key contributions of our research are: 1) proving the convergence of the algorithm to an optimal solution given a mild assumption on the initial condition; 2) showing that the well-known cross-entropy optimization algorithm is a special case of CWO-based algorithms. To the best knowledge of the author, there is no previous convergence proof for the cross-entropy method. In practice, numerical experiments have demonstrated that a CWO-based algorithm can find a better solution than the cross-entropy method. Finally, in the future, we would like to apply some of the ideas from cumulative prospect theory to games. In this thesis, we present a numerical example where cumulative prospect theory has an unexpected effect on the equilibrium points of the classic prisoner's dilemma game.