Due to high penetration of renewable energy resources in today's electricity generation, considerable voltage fluctuations are witnessed in power systems. As an attempt to solve this issue, in this study, multi-objective optimal placement and sizing of distribution-level battery storage system is performed using semidefinite programming. Placement of one or multiple battery system is studied under various objectives including the cost, voltage regulation, reactive power dispatch, renewable resource curtailment, and minimum network power losses. Power flow equations are solved in the form of semidefinite constraints and the rank constraint is ignored. Additionally, combination of these objectives to form a multi-objective problem and regularization of the number of battery sites are studied. Finally, simulation results are provided to analyze the proposed formulation.