Although these decomposition algorithms are very efficient, they are offline algorithms, where the future demand information is needed.However, this type of information is not available before the end of the whole period in reality.
Then, based on these results, we propose a distributed online algorithm for solving the OPF problem, where no precise knowledge of future demands are required in contrast to the existing approach.
We use the competitive ratio to show the theoretical performance of the online algorithm.
First, we study the optimal power flow (OPF) in ac-dc grids, which is a non-convex optimization problem.
We use convex relaxation techniques and transform the problem into a semidefinite program (SDP).
The results demonstrate the capabilities of the proposed MOPSO technique to generate a set of well-distributed Pareto-optimal solutions in one single run.
In smart grid, the penetration of two-way flows of electricity and information makes it capable of integrating distributed renewable energy sources (RES) and a large number of demand side users much more effectively.We introduce the concept of conditional value-at risk to limit the net power supply shortage. The SCUC is a nonlinear mixed-integer optimization problem. The proposed MOPSO technique has been implemented to solve the OPF problem with competing and non-commensurable cost and voltage stability enhancement objectives.The optimization runs of the proposed approach have been carried out on a standard test system.We derive the sufficient conditions for zero relaxation gap and design an algorithm to obtain the global optimal solution. Subsequently, we study the security-constrained unit commitment (SCUC) problem in ac-dc grids with generation and load uncertainty. The decomposition methods offer new interesting insights on the equilibrium load profile smoothing feature over space and time through the relationship between the optimal dual solution in the OPF and the energy storage dynamics.We investigate the energy storage dynamics under different problem settings and verify that the distributed algorithms can converge fast to the global optimal solution by numerical simulations in IEEE test systems.Through extensive simulations in the IEEE 14-bus system, we show that the algorithm can converge fast to the optimal solution.Moreover, the actual ratio between the online algorithm result and the offline optimal value is less than 1.2 by properly choosing the system parameters.