On-load tap changer (OLTC) is essential in regulating the operation status of power transformers employed in modern power systems. While exploring power flow analysis, electromagnetic and electromechanical simulations by using the on-load tap changer, it is found that inaccuracy problem may occur with the assumption in conventional transformers that tap positions only affect the turns ratio parameter; however, the real transformers specifications, such as the resistances and inductances of windings, also fluctuate with different tap positions. In this paper, a novel inductance matrix model for both single and three phase transformer is proposed, which illustrates that winding resistances and inductances are also varying with the tap positions. Case studies are performed to assess the performance of the proposed transformer model in case of symmetrical and un-symmetrical faults. The novel model is developed using PSCAD/EMTDC software, and the simulation results are compared with traditional transformers. It can be concluded that the parameters of the proposed transformer become more sensitive on the voltage and current during various transient processes. Thus it's vital to provide an applicable attention to the analysis and simulation with the usage of this more accurate mathematical transformer model, which permits us to obtain the more precise behavior of power systems without any risk.