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Flexible Demand Management under TimeVarying Prices
 Liang, Yong
 Advisor(s): Shen, ZuoJun M
Abstract
In this dissertation, the problem of flexible demand management under timevarying prices is studied. This generic problem has many applications, which usually have multiple periods in which decisions on satisfying demand need to be made, and prices in these periods are timevarying. Examples of such applications include multiperiod procurement problem, operating room scheduling, and userend demand scheduling in the Smart Grid, where the last application is used as the main motivating story throughout the dissertation.
The current grid is experiencing an upgrade with lots of new designs. What is of particular interest is the idea of passing timevarying prices that reflect electricity market conditions to end users as incentives for load shifting. One key component, consequently, is the demand management system at the userend. The objective of the system is to find the optimal tradeoff between cost saving and discomfort increment resulted from load shifting. In this dissertation, we approach this problem from the following aspects: (1) construct a generic model, solve for Pareto optimal solutions, and analyze the robust solution that optimizes the worstcase payoffs, (2) extend to a distributionfree model for multiple types of demand (appliances), for which an approximate dynamic programming (ADP) approach is developed, and (3) design other efficient algorithms for practical purposes of the flexible demand management system.
We first construct a novel multiobjective flexible demand management model, in which there are a finite number of periods with timevarying prices, and demand arrives in each period. In each period, the decision maker chooses to either satisfy or defer outstanding demand to minimize costs and discomfort over a certain number of periods. We consider both the deterministic model, models with stochastic demand or prices, and when only partial information about the stochastic demand or prices is known. We first analyze the stochastic optimization problem when the objective is to minimize the expected total cost and discomfort, then since the decision maker is likely to be riskaverse, and she wants to protect herself from price spikes, we study the robust optimization problem to address the riskaversion of the decision maker. We conduct numerical studies to evaluate the price of robustness.
Next, we present a detailed model that manages multiple types of flexible demand in the absence of knowledge regarding the distributions of related stochastic processes. Specifically, we consider the case in which timevarying prices with general structures are offered to users, and an energy management system for each household makes optimal energy usage, storage, and trading decisions according to the preferences of users. Because of the uncertainties associated with electricity prices, local generation, and the arrival processes of demand, we formulate a stochastic dynamic programming model, and outline a novel and tractable ADP approach to overcome the curses of dimensionality. Then, we perform numerical studies, whose results demonstrate the effectiveness of the ADP approach.
At last, we propose another approximation approach based on Qlearning. In addition, we also develop another decentralizationbased heuristic. Both the Qlearning approach and the heuristic make necessary assumptions on the knowledge of information, and each of them has unique advantages. We conduct numerical studies on a testing problem. The simulation results show that both the Qlearning and the decentralization based heuristic approaches work well. Lastly, we conclude the paper with some discussions on future extension directions.
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