This dissertation, "Energy Management in Power Grid With Power Flow Routing" by Junhao, Lin, 林俊豪, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: The increase in energy demand and the integration of intermittent renewable energy sources (RESs) are stressing the power grid, prompting system operators to take active control measures for managing the power flow more efficiently and intelligently. Power flow routing, an emerging control paradigm for the flexible and responsive control of power flows, is a promising solution for power flow control and energy management. While most existing research efforts have been devoted to the hardware implementation of power flow controllers (PFCs) and power flow routers (PFRs), a systematic modelling and optimization framework is desired to facilitate the network-level research on power flow routing. In this thesis, we focus on the steady-state analysis and energy management for the future power network integrated with PFCs and PFRs. First, a generic functional model of the PFR is developed and incorporated into the optimal power flow (OPF) framework. The proposed PFR model encapsulates the desired features of PFRs, and is amenable for implementation of power flow routing. To pursue global optimality, a semidefinite programming (SDP) relaxation of the PFR-OPF problem is developed with a regularization method to guide a rank-1 solution. The numerical study on the assessment of the system loadability shows that the integration of PFRs and PFCs can improve the loadability significantly, and that the proposed SDP relaxation succeeds in obtaining the optimal or near-optimal solution of the PFR-OPF problem. Second, we study the robust dispatch of energy supply and spinning reserve to overcome the uncertainty of renewable generation. Based on the PFR-OPF framework, a robust OPF problem that incorporates power flow routing is formulated and solved by a column-and-constraint generation (C&CG) algorithm. A second-order cone programming relaxation is applied to the non-convex alternating-current (AC) power flow regions with the phase angle constraints for loops retained by linear approximation. Numerical results show the efficacy of our robust dispatch strategy in guaranteeing immunity against uncertain renewable generation, as well as in reducing the energy management costs through power flow routing. Finally, the robust OPF framework is extended to a multi-period robust OPF framework with receding horizon control to further cope with the variability of renewables. A robust resource scheduling problem for the direct-current (DC) microgrid is formulated to jointly optimize the power injections of distributed energy resources (DERs) and the configurations of PFCs and PFRs. Numerical results show that the proposed robust scheduling method is able to adapt to the fluctuations and variations of renewable generation in real time, and to achieve robustness guarantee with negligible loss of optimality. Empirically, with just a few PFCs and PFRs installed, the system can already achieve remarkable reduction of energy management costs. Subjects: Electric power systems - Automatic control Distributed generation of electric power - Computer simulation