Electric grid is undergoing a profound transition to achieve several targets such as a more efficient transmission of electricity, lower carbon emissions and an improved security. During this transition, there are a lot of challenges to be tackled, including both traditional ones such as the optimal power flow related problems and new ones that consider an increasing integration of renewable energy sources. This dissertation studies various energy related optimization problems in smart grids and develops models and algorithms to improve the efficiency and the flexibility of power systems.

In the first part of this thesis, we propose a solution framework to deal with one of the fundamental problems in power systems. It has been shown that many computationally difficult problems...[ Read more ]

Electric grid is undergoing a profound transition to achieve several targets such as a more efficient transmission of electricity, lower carbon emissions and an improved security. During this transition, there are a lot of challenges to be tackled, including both traditional ones such as the optimal power flow related problems and new ones that consider an increasing integration of renewable energy sources. This dissertation studies various energy related optimization problems in smart grids and develops models and algorithms to improve the efficiency and the flexibility of power systems.

In the first part of this thesis, we propose a solution framework to deal with one of the fundamental problems in power systems. It has been shown that many computationally difficult problems can be equivalently reformulated into quadratically constrained quadratic programs (QCQPs) in the literature of power systems. Semidefinite programming (SDP) relaxation has been widely used to solve QCQPs. However, how to recover a near optimal rank-one solution from the results obtained in the SDP relaxation is a critical issue. In view of this, we design an algorithm to obtain rank-one solutions for the SDP relaxation of QCQPs in power systems.

In the second part of this thesis, we consider the energy management problem for cooperative microgrids (MGs). The cooperation of multiple MGs by direct energy exchange among neighboring MGs can help alleviate the local mismatch of supply and demand within MGs. Therefore, the coordinated energy management problem of networked MGs has been studied.

In the third and fourth parts of this thesis, we design a market in the transmission network for the load aggregators with multi-dimensional flexibility (MDF), and study how to exploit the MDF of loads to balance the trade-off between generation cost and system risks related to wind curtailment and power deficiency.