The performance characteristics of a multilevel three-phase solid state shunt active filter (SAF) is explored in this study as part of a high power electrical system in more-electric-aircraft (MEA) power architecture. The proposed SAF is based on modular multilevel converter (MMC) topology that would be used to track and compensate the harmonic contents of the load currents in an aircraft power distribution system. The implementation of the SAF is conducted with current control scheme utilizing finite control set-model predictive control (FCS-MPC) algorithm. This research describes how the computational efficiency of the predictive current controller can be enhanced with the use of an integrated perturbation analysis and sequential quadratic programming (IPA-SQP) solver, which in turn reduces the constraints imposed upon the system optimization and sampling. The design and development procedures of the current control algorithm are discussed along with the validation processes used in a five-level three-phase shunt active power filter topology. The key emphasis on system transients and steady-state behaviors is considered through variations in loads, supply impedances and operating frequencies.