International Journal of Mathematical, Engineering and Management Sciences Vol. 5, No. 5, 939-956, 2020 https://doi.org/10.33889/IJMEMS.2020.5.5.072 939 Reduction of Large-Scale Dynamical Systems by Extended Balanced Singular Perturbation Approximation Santosh Kumar Suman Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, India. Corresponding author: sksumanee@gmail.com Awadhesh Kumar Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, India. E-mail: awadhesg26@gmail.com (Received December 31, 2019; Accepted May 9, 2020) Abstract A simplified approach for model order reduction (MOR) idea is planned for better understanding and explanation of large- scale linear dynamical (LSLD) system. Such approaches are designed to well understand the description of the LSLD system based upon the Balanced Singular Perturbation Approximation (BSPA) approach. BSPA is tested for minimum / non-minimal and continuous/discrete-time systems valid for linear time-invariant (LTI) systems. The reduced-order model (ROM) is designed to preserved complete parameters with reasonable accuracy employing MOR. The Proposed approach is based upon retaining the dominant modes (may desirable states) of the system and eliminating comparatively the less significant eigenvalues. As the ROM has been derived from retaining the dominant modes of the large- scale linear dynamical stable system, which preserves stability. The strong aspect of the balanced truncation (BT) method is that the steady-state values of the ROM do not match with the original system (OS). The singular perturbation approximation approach (SPA) has been used to remove this drawback. The BSPA has been efficaciously applied on a large-scale system and the outcomes obtained show the efficacy of the approach. The time and frequency response of an approximated system has been also demonstrated by the proposed approach, which proves to be an excellent match as compared to the response obtained by other methods in the literature review with the original system. Keywords- MOR, Large-scale linear dynamical system, Balanced truncation method, Steady state value, Singular perturbation approximation. 1. Introduction The major issue in any aspect of a higher dimension systems dynamic behaviour is all over and occurs in different fields, including some engineering applications, e.g. Electrical Power system, control engineering, system design, smart city, transportation device and ecological systems, etc. ( Sikander and Prasad, 2015; Sambariya and Sharma, 2016; Daraghmeh and Qatanani, 2018; Suman and Kumar, 2019). The complex large-scale mathematical system must contain a comprehensive description of the original system (Daraghmeh et al., 2019). This mainly consists of many forms of differential and algebraic equations (Sikander and Prasad, 2015; Kumar et al., 2019). Conventional numerical modelling procedures cannot maintain the various queries as per necessity in applications that are, where the large system must be frequently used to find the solution. It is quite common that after several days, one solution has not yet been obtained. The reduction of the large- scale LTI system using MOR has proven to be quite promising to get a stable solution much more quickly. The MOR is a key branch of complex system and control concept, that studies the characteristics of LSLD systems in the need to reduce the trouble while retaining their input-output behaviour intact (Chaturvedi, 2018). The key objective of MOR is to replicate the significant