An exclusive model order reduction (MOR) technique for a discrete-time (DT) index 2 dynamical structure is examined in this work. The power systems model can be considered a common model for control issues and controller design, and these models have relatively large dimensions. The cross gramian (CG) may be used to evaluate the key input-output characteristics of such systems CG. Computing the gramians using the traditional analytic approach can be time-consuming and next to impossible in certain cases. Hence, in the last few decades a lot of attention received on iterative approaches. The iterative approach proposed is focused on factored approximations of the CG, which are accomplished by alternating directional implicit (ADI) methods. We use the factors to derive a congruent reduced model of a discrete-time index-2 system. To demonstrate the effectiveness and correctness of our proposed approach, frequency response simulations are presented in a numerical example. Reduction of the structured model of discrete-time index 2 structures can now be accomplished using this method.