This digest presents a computationally efficient multi-objective direct model predictive control of grid-tied 3L-ANPC with an output LCL filter. Direct MPC allows fast and decoupled control of state-variables through a user defined cost function. However, the state-variable predictions require iteration of 27 switching vectors which increases the computational burden (CB), making the deployment of the controller infeasible to low-cost mass-marketed DSPs. Presented method restricts the number of switching states being checked through the presented criteria. The limitation reduces the number of states being checked from 27 to just 8 at maximum, making the CB identical to six switch 2L-VSC.