A multiturn injection scheme is used in the XiPAF-upgrading synchrotron, with beam loss mainly occurring at the injection septum. The paper presents two theoretical models for calculating the efficiency of multiturn injection in compact synchrotrons, with a focus on the situation of dispersion mismatch at the injection point. The first model is the beam phase ellipse rotation model, which is based on the beam projection distribution. The second model is the injection septum rotation model, which is based on the particle coordinate criterion. The deviation in efficiency between both injection models and the simulation results is less than 5%, and the calculation speed has increased by a factor of 1000 compared to PyORBIT simulations. The models are used to optimize the multiturn injection efficiency of the XiPAF-upgrading synchrotron, resulting in an optimal injection efficiency of 92%.