  In order to unifiedly coordinate economy and voltage deviations, a novel
multi-objective optimal power flow (MOPF) algorithm is proposed for an AC/DC
system with VSC-HVDC based on cooperative multi-objective particle swarm
optimization (CMOPSO). In order to minimize power generation costs and voltage
deviations, the MOPF model of the AC/DC system is firstly built based on the
VSC-HVDC steady-state model. Then, the CMOPSO is adopted for solving the MOPF
model to find well-distributed Pareto-optimal solutions. Next, the solutions
are divided into different groups via the fuzzy C-means algorithm, and finally
the best compromise solutions reflecting decision-makers' different preferences
are identified from each group by comparing the priority memberships which are
calculated by using the grey relation projection method. The validity of the
proposed approach is verified by using the modified IEEE 14-bus and 118- bus
systems.
