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.

In this, a new Higher-Order Reduction (HOR) scheme is proposed for better understanding and explanation of a large-scale dynamical (LSD) system. This proposed scheme is based on a balanced realization method (BRM) in which the steady-state gain issue of the BRM is circumvented. This method guarantees that the system is stable and preserved static behaviour. The reduced-order model (ROM) is calculated to maintain entire parameters with fair accuracy by model order reduction (MOR). Further, in terms of transient and frequency responses, the performance of the proposed scheme is analysed. In this paper, we have used two approaches that are balanced realization method (BRM) and stability equation method (SEM) for HOR. According to that procedure, the denominator coefficients (DC) of the reduced model is obtained by BRM and the numerator coefficients (NC) are computed by SEM. This technique gives the least performance error indices compared to some another existing approaches through a literature review. Additionally, the control action is obtained by using the genetic algorithm (GA) based PID (proportional integral derivative) controller has been proposed. In this tuning optimized PID parameters done using of objective functions, the concept of error minimisation (performance index). As the proposed approach is used both in the simplification of systems and in the design of controller, therefore it may be applied in various applications of LSD system analysis and design. The proposed scheme is proved by a numerical example. ‫العلوم‬ ‫فرع‬ ‫فيصل،‬ ‫امللك‬ ‫لجامعة‬ ‫العلمية‬ ‫املجلة‬ ‫والطبيعية‬ ‫األساسية‬ ، ‫الطباعة)‬ ‫(بانتظار‬ ‫العدد‬ ‫الطباعة)،‬ ‫(بانتظار‬ ‫املجلد‬

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Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

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