This thesis addresses an optimal current operation strategy and harmonic interaction analysis of delta-connected cascaded H-bridge (CHB) multilevel converter based shunt active power filter (APF). An optimal current operation strategy for a delta-connected CHB based shunt APF under non-ideal grid conditions is presented that minimizes the shunt APF apparent power and satisfies requirements on average power balance, power factor constraint, source current distortion and imbalance characteristics in compliance with grid codes. The optimization problem is formulated using a convex quadratic objective function and non-convex quadratic constraints and solved by sequential convex programming (SCP). The presented harmonic interaction analysis is based on the derivation of a time-invariant model in dq-frame from a time-varying model in abc-frame. In the derived time-invariant model, the symmetrical components of each frequency order in the shunt APF variables can be decoupled while preserving the interaction with other variables. The harmonic interaction analysis technique is able to predict how harmonics propagate through the system and quantify the shunt APF variables. The proposed current strategy and harmonic interaction analysis are evaluated by simulations in comparison with related approaches from literature, to demonstrate the effectiveness.