Increasing the Reliability of Power and Communication Networks via Robust Optimization

Uncertainty plays an increasingly significant role in the planning and operation of complex networked infrastructure. The inclusion of variable renewable energy in power systems makes ensuring basic grid requirements such as transmission line constraints and the power balance between supply and demand more involved. Likewise, data traffic in communication networks varies greatly with user preferences and service availability, and with communication networks carrying more traffic than ever due to the surge in network-enabled devices, coping with the highly variable data flows between server and end-users becomes more crucial for the network's overall stability. Within this context, we propose in this thesis new adaptable methods for optimizing flows in power and communication systems that explicitly consider the growing variability in these systems to guarantee optimal operation with a flexible degree of reliability. The proposed methods use a robust optimization framework, making constraints dependent on uncertain factors tractable by replacing originally stochastic conditions with deterministic counterparts. The primary benefit of robust methods is that they ensure the system is feasible for any values of the uncertain variables within a given continuous set of possible realizations. This, however, can lead to excessively conservative solutions. Therefore, we also investigate how to reduce the conservativeness of the proposed algorithms. This thesis focuses on two classes of problems in power and communication systems, flow control and the placement of flow-controlling devices. In power systems, flow control refers to actions that induce changes in the power carried by transmission lines to minimize or maximize a specific objective value while considering the electrical grid's physical constraints. Some examples of power flow control actions are the change of switching equipment's state, regulation of generators' set points, and the management of the so-called Flexible AC Transmission Systems (FACTS) devices. For the last two action types, we propose a robust approach to optimize the corresponding control policies. As for communication networks, (data) flow control is implemented at each router in the network. These routers define the path and the rate data is forwarded using routing tables. We show that it is possible to robustly design policies to adapt these routing tables that optimize the data flows in the network depending on the instantaneous rate of the system's exogenous inputs. For both flow problems, we employ a robust optimization framework where affine-linear functions parametrize the flow control policies. The parametrized policies can be efficiently computed via linear or quadratic programming, depending on the system's constraints. Furthermore, we consider the placement problems in the form of FACTS placement and the embedding of virtual networks in an existing communication network to improve the reliability of the network systems. Both problems are formulated as robust Mixed-Integer Linear Programs (MILP). However, because finding provable optimal solutions in large networks is computationally challenging, we also develop approximate algorithms that can yield near-optimal results while being several times faster to solve than the original MILP. In the proposed robust framework, the flow control and the placement of controlling-devices problems are solved together to take into account the coupling effects of the two optimization measures. We demonstrate the proposed methodology in a series of use cases in power and communication systems. We also consider applications in Smart Grids, where communication and electric networks are closely interlinked. E.g., communication infrastructure enables real-time monitoring of the status of power grids and sending timely control signals to devices controlling the electric flow. Due to the increasing number of renewable energy resources, Smart Grids must adapt to fast changes in operating conditions while meeting application-dependent reliability requirements. The robust optimization methods introduced in this thesis can thus use the synergy between flexible power and communication systems to provide secure and efficient Smart Grid operation