Dynamic-Data Driven Real-Time Identification for Electric Power Systems

Power system engineers face a double challenge: to operate electric power systems within narrow stability and security margins, and to maintain high reliability. There is an acute need to better understand the dynamic nature of power systems in order to be prepared for critical situations as they arise. Innovative measurement tools, such as phasor measurement units, can capture not only the slow variation of the voltages and currents but also the underlying oscillations in a power system. Such dynamic data accessibility provides us a strong motivation and a useful tool to explore dynamic-data driven applications in power systems. To fulfill this goal, this dissertation focuses on the following three areas: Developing accurate dynamic load models and updating variable parameters based on the measurement data, applying advanced nonlinear filtering concepts and technologies to real-time identification of power system models, and addressing computational issues by implementing the balanced truncation method. By obtaining more realistic system models, together with timely updated parameters and stochastic influence consideration, we can have an accurate portrait of the ongoing phenomena in an electrical power system. Hence we can further improve state estimation, stability analysis and real-time operation.

Coordinated pricing and inventory management

This dissertation mainly focuses on coordinated pricing and inventory management problems, where the related background is provided in Chapter 1. Several periodic-review models are then discussed in Chapters 2,3,4 and 5, respectively. Chapter 2 analyzes a deterministic single-product model, where a price adjustment cost incurs if the current selling price is changed from the previous period. We develop exact algorithms for the problem under different conditions and find out that computation complexity varies significantly associated with the cost structure. %Moreover, our numerical study indicates that dynamic pricing strategies may outperform static pricing strategies even when price adjustment cost accounts for a significant portion of the total profit. Chapter 3 develops a single-product model in which demand of a period depends not only on the current selling price but also on past prices through the so-called reference price. Strongly polynomial time algorithms are designed for the case without no fixed ordering cost, and a heuristic is proposed for the general case together with an error bound estimation. Moreover, our illustrates through numerical studies that incorporating reference price effect into coordinated pricing and inventory models can have a significant impact on firms' profits. Chapter 4 discusses the stochastic version of the model in Chapter 3 when customers are loss averse. It extends the associated results developed in literature and proves that the reference price dependent base-stock policy is proved to be optimal under a certain conditions. Instead of dealing with specific problems, Chapter 5 establishes the preservation of supermodularity in a class of optimization problems. This property and its extensions include several existing results in the literature as special cases, and provide powerful tools as we illustrate their applications to several operations problems: the stochastic two-product model with cross-price effects, the two-stage inventory control model, and the self-financing model.