Embedded with producers, consumers, and prosumers, active Low-Voltage Distribution Networks (LVDNs) with bi-directional power flows are rising to over-shadow the investment and operation planning in power systems. The Optimal Power Flow (OPF) has been extensively used in the recent years to solve different investment and operation planning problems in LVDNs. However, OPF is inherently a complex non-linear and non-convex optimization problem. Hence, different linearization and convexification models have been introduced in the literature to enhance the modeling accuracy and computational tractability of the OPF problem in LVDNs. In this paper, five multi-period OPF models (including the basic non-linear and non-convex one) are presented, with different linearizations/convexifications for the power flow equations. The proposed models are implemented on the IEEE 34-bus test system and their modeling accuracy and computational complexity are compared and discussed.