This paper presents the three new pin-resolved transient solvers of PROTEUS-MOC developed in a consistent way to the latest steady-state solver. A new transient fixed source problem (TFSP) solver was developed without relying on the isotropic approximation of the angular flux time derivative. A moving axial mesh scheme was also implemented to model the control rod movement accurately with coarse axial meshes. In addition, in order to reduce the computational time further, an improved quasi-static method (IQM) solver and a predictor-corrector quasi-static method (PCQM) solver were developed in a consistent way to the TFSP solver. Initial verification tests were performed using the C5G7-TD benchmark problems. The results of the direct TFSP solver agreed very well with the MPACT and NECP-X solutions within ~2.5%. Additional analyses suggested that the observed differences are mainly due to the coarse time steps used in the MAPCT and NECP-X calculations. These results indicate that the direct TFSP solver of PROTEUS-MOC was correctly implemented and the moving axial mesh scheme is working properly. Numerical tests of IQM and PCQM against the direct TFSP solver showed that the IQM and PCQM solvers can reduce the computational time about 10 to 100 times without any significant loss of accuracy by allowing larger time steps. The PCQM calculation with the quadratic interpolation of kinetics parameters (KPs) showed the best performance among the four combinations of the IQM and PCQM solvers and the linear and quadratic interpolation schemes of KPs. This study also showed that the different delayed neutron precursor models of six and eight families can cause larger power differences than the different high-fidelity transient codes and that the adjoint scalar flux weighting can cause significant errors in KPs and subsequently in power evolution. In addition, the transient analyses of a modified C5G7 benchmark problem containing a void channel similar to the hodoscope channel of the Transient Reactor Test (TREAT) facility showed that the isotropic approximation of the angular flux time derivative can cause nonnegligible errors in the time-dependent power distribution. This study also demonstrated that PROTEUS-MOC can be used for transient analyses of reactors with internal void regions.