Spatial and temporal hierarchical decomposition methods for the optimal power flow problem

Abstract

The subject of this thesis is the development of spatial and temporal decomposition methods for the optimal power flow problem, such as in the transmissiondistribution network topologies. In this context, we propose novel decomposition interfaces and effectivemethodology for both the spatial and temporal dimensions applicable to linear and non-linear representations of the OPF problem.

These two decomposition strategies are combined with a Benders-based algorithmand have advantages in model building time, memory management and solving time. For example, in the 2880-period linear problems, the decomposition finds optimal solutions up to 50 times faster and allows even larger instances to be solved; and in multi-period non-linear problems with 48 periods, close-to-optimal feasible solutions are found 7 times faster.

With these decompositions, detailed networks can be optimized in coordination, effectively exploiting the value of the time-linked elements in both transmission and distribution levels while speeding up the solution process, preserving privacy, and adding flexibility when dealing with different models at each level.

In the non-linear methodology, significant challenges, such as active set determination, instability and non-convex overestimations, may hinder its effectiveness, and they are addressed, making the proposed methodology more robust and stable. A test network was constructed by combining standard publicly available networks resulting in nearly 1000 buses and lines with up to 8760 connected periods; several interfaces were presented depending on the problemtype and its topology using a modified Benders algorithm. Insight was given into why a Benders-based decomposition was used for this type of problem instead of a common alternative: ADMM.

The methodology is useful mainly in two sets of applications: when highly detailed long-termlinear operational problems need to be solved, such as in planning frameworks where the operational problems solved assume no prior knowledge; and in full AC-OPF problems where prior information from historic solutions can be used to speed up convergence.