  A two-stage solution approach for solving the problem of multi-objective
optimal power flow (MOPF) is proposed for hybrid AC/DC grids with VSC-HVDC.
First, a MOPF model for hybrid AC/DC grids is built to coordinate the economy,
voltage deviation and environmental benefits. Then, a two-stage solution
approach, incorporating decision analysis into optimization process, is
presented to solve the model. The first stage of the approach is consisted of a
multi-objective particle swarm optimization algorithm with a hybrid coding
scheme employed to find multiple Pareto-optimal solutions. The second stage
will have the obtained solutions clustered into different groups using fuzzy
c-means (FCM) clustering, and then the 'best' compromise solutions are obtained
by calculating the priority memberships of the solutions belonging to the same
groups via grey relation projection (GRP) method. The novelty of this approach
lies primarily in incorporating the FCM-GRP based decisions analysis technique
into MOPF studies, thereby assisting decision makers to automatically identify
the 'best' operation points. The effectiveness of the proposed approach is
verified based on the test results of the IEEE 14- and 300- bus systems.
