Advances in Electric Power Systems : Robustness , Adaptability , and Fairness

The electricity industry has been experiencing fundamental changes over the past decade. Two of the arguably most significant driving forces are the integration of renewable energy resources into the electric power system and the creation of the deregulated electricity markets. Many new challenges arise. In this thesis, we focus on two important ones: How to reliably operate the power system under high penetration of intermittent and uncertain renewable resources and uncertain demand: and how to design an electricity market that considers both efficiency and fairness. We present some new advances in these directions. In the first part of the thesis, we focus on the first issue in the context of the unit commitment (UC) problem, one of the most critical daily operations of an electric power system. Unit commitment in large scale power systems faces new challenges of increasing uncertainty from both generation and load. We propose an adaptive robust model for the security constrained unit commitment problem in the presence of nodal net load uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and outer approximation techniques. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England (ISO-NE). Computational results demonstrate the advantages of the robust model over the traditional reserve adjustment approach in terms of economic efficiency, operational reliability, and robustness to uncertain distributions. In the second part of the thesis, we are concerned with a geometric characterization of the performance of adaptive robust solutions in a multi-stage stochastic optimization problem. We study the notion of finite adaptability in a general setting of multi-stage stochastic and adaptive optimization. We show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions. Ve show that a class of finitely adaptable solutions is a good approximation for both the multi-stage stochastic as well as the adaptive optimization problem. To the best of our knowledge, these are the first approximation results for multi-stage problems in such generality. Moreover, the results and the proof techniques are quite general and extend to include important constraints such as integrality and linear conic constraints. In the third part of the thesis, we focus on how to design an auction and pricing scheme for the day-ahead electricity market that achieves both economic efficiency and fairness. The work is motivated by two outstanding problems in the current practice the uplift problem and equitable selection problem. The uplift problem is that the electricity payment determined by the electricity price cannot fully recover the production cost (especially the fixed cost) of some committed generators, and therefore the ISOs make side payments to such generators to make up the loss. The equitable selection problem is how to achieve fairness and integrity of the day-ahead auction in choosing from multiple (near) optimal solutions. We offer a new perspective and propose a family of fairness based auction and pricing schemes that resolve these two problems. We present numerical test result using ISO-NE's day-ahead market data. The proposed auctionpricing schemes produce a frontier plot of efficiency versus fairness, which can be used as a vaulable decision tool for the system operation. Thesis Supervisor: Dimitris Bertsimas Title: Boeing Leaders for Global Operations Professor