This paper addresses the complexity and nonlinear dynamics that may arise in solid state transformers (SST). SST in contrast to the conventional transformer is prone to nonlinear and complex dynamics due to incorporation of power electronic (PE) converter and devices. This is because of nonlinear nature, interdependence and coupling, and feedbacks (e.g. control) of these converters. In this paper, the nonlinear and complex behavior of a SST connected to the power grid will be investigated by presenting some test results in normal or extreme operation of system. Then a methodology of complexity quantification will be proposed, which is a refinement of a popular measure called approximate entropy (ApEn). This methodology will be used to interpret some complex behavior of SST system. The detailed model and control scheme of SST including AC/DC rectifier, Dual Active Bridge (DAB) converter and DC/AC inverter are developed to enable dynamic system level simulation.