This paper proposes a distributed control scheme for the economic dispatch of islanded AC microgrids. The control goal is the economical power-sharing of distributed generators considering the marginal cost of active and reactive power. The controller is developed in a finite-time protocol over a droop-free strategy, without restoration needs for frequency. Simulations through the software PLECS are provided for validation purposes; they show adequate behaviour of the controllers under impact loads and plug & play operation.