Robust optimization for renewable energy integration in power system operations

Optimization provides critical support for the operation of electric power systems. As power systems evolve, enhanced operational methodologies are required, and innovative optimization models have the potential to support them. The need for sustainability has led to many transformations, including the deep adoption of wind and solar energy in many power systems. These renewable energy sources have tremendous environmental benefits and can be very convenient economically, however, the power supply they provide is highly uncertain and difficult to predict accurately. This Thesis proposes Robust Optimization models and algorithms for improving the management of uncertainty in electric power system operations. The main goal is to devise new operational methodologies to support the integration of variable renewable energy sources. The first part of this Thesis presents the development of an adaptive robust optimization model for the economic dispatch problem under uncertainty in wind power. The goal of this problem is to determine the power output levels of generating units in order to minimize costs while satisfying several technical constraints. The concept of dynamic uncertainty set is developed to account for temporal and spatial correlations in wind speeds. Further, a simulation platform is implemented to combine the dispatch model with statistical prediction tools in a rolling-horizon framework. Extensive numerical experiments are carried out on this platform using real wind data, showing the potential benefits of the proposed approach in terms of cost and reliability improvements over deterministic models and simpler robust optimization models that ignore temporal and spatial correlations. The second part proposes a multistage adaptive robust optimization model for the unit commitment problem, under uncertainty in nodal net loads. The purpose of this problem is to schedule available generating capacities in each hour of the next day, including on/off generator decisions. The proposed model takes into account the time causality of the hourly unfolding of uncertainty in the power system operation process, which is shown to be relevant when ramping capacities are limited and net loads present significant variability. To deal with large-scale systems, the idea of simplified affine policies is explored and a solution method based on constraint generation is developed. Extensive computational experiments on a 118-bus test case and a real-world power system with 2736 buses demonstrate that the proposed algorithm is effective in handling large-scale power systems and that the proposed multistage robust model can significantly outperform a traditional deterministic model and an existing two-stage robust model in both operational cost and system reliability. The third part develops a more sophisticated multistage robust unit commitment model, where the temporal and spatial correlations of wind and solar power are considered, as well as energy storage devices. A new specialized simplified affine policy is proposed for dispatch decisions, and an efficient algorithmic framework using a combination of constraint generation and duality based reformulation with various improvements is developed. Extensive computational experiments show that the proposed method can efficiently solve the problem on a 2736-bus system under high dimensional uncertainty of 60 wind farms and 30 solar farms. The computational results also suggest that the proposed model leads to significant benefits in both costs and reliability over robust models with traditional uncertainty sets as well as deterministic models with reserve rules. Finally, the fourth part explores how to jointly consider the non-convexity of the power flow equations and the uncertainty in renewable outputs in power dispatch problems. Here, a two-stage adaptive robust optimization model is developed for the alternating current optimal power flow problem, considering multiple time periods and including technical details such as transmission line capacities and the reactive capability curves of conventional generators and renewable units. To solve this challenging problem, it is proposed to use convex relaxations and an alternating direction method to identify worst-case uncertainty realizations. Further, a speed-up technique based on screening transmission line constraints is explored. Extensive computational experiments show that the solution method is efficient and that there are significant advantages both from the economic and reliability standpoints as compared to a deterministic model for this problem.Ph.D