Stochastic Optimization and Optimal Control for Complex Networked Infrastructures

Networked infrastructures (e.g., power grids and water networks) are becoming increasingly complicated systems due to accelerating integration of distributed devices, increasing scale of network systems, heterogeneous distributed control strategies, nonlinear nature of physical models and unpredictable netloads (e.g., renewable energy and water demands). These tendencies promise to deliver unprecedented flexibility and smart features in these systems, but require more sophisticated modelling and operation schemes. In particular, the large and unpredictable uncertainties across networks are challenging the current management and threaten the security of these vital infrastructures. The main goal of this dissertation is to establish a methodology for designing stochastic operation strategies in complex networks with large variation uncertainties, for optimal performance, stability and robustness, which is applicable to a wide range of networked infrastructures. This dissertation addresses the main goal in various time-scales, ranging from the operation phase in minutes to the dynamic phase in seconds. In the operation phase, we present a data-based distributionally robust stochastic optimal control framework to attain the real-time optimal adjustment for controllable devices based on a finite training dataset of uncertainties. We consider ambiguity sets of probability distributions centered around the finite sampling dataset, and leverage Wasserstein metric to quantify the distance between the empirical data-based distribution and the real unknown data-generating distribution. This allows the optimal decisions to be robust to the worst case probability distribution within the ambiguity sets, which efficiently trades off efficiency, risks of constraint violations and out-of-sample performance. This proposed framework is adapted to solve the stochastic optimal power flow (OPF) problems for power systems (i.e., transmission systems and distribution networks) and the stochastic optimal water pump control for water distribution networks. In addition, we propose a gradient-based optimal control algorithm with state estimation in the loop to facilitate the practical implementation of OPF problems in large-scale distribution networks, where has inadequate monitoring and unreliable measurement infrastructures. In the dynamic phase, we consider the linear system with multiplicative noise and additive noise, which captures the modelling errors and netload uncertainties, respectively. We adapt this model to study the performance and stability of low-inertia power grids with stochastic system inertia. An analytical expression of system H2 norm is provided and a mean-square stability criteria is developed. In addition, we present a multi-stage stochastic optimal control problem for wind farm power maximization. We generalize the original actuator disk model (ADM) by incorporating state- and input-dependent multiplicative noises as a stochastic actuator disk model (S-ADM) to capture the stochastic wind fluctuations. The optimal control policies for each wind turbine explicitly incorporate the moment information of multiplicative noise, which establishes a connection between uncertainties sampling dataset and optimal feedback control.