Indonesian Journal of Electrical Engineering and Computer Science Vol. 25, No. 1, January 2022, pp. 51~58 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v25.i1.pp51-58  51 Journal homepage: http://ijeecs.iaescore.com An analytical approach for LQR design for improving damping performance of multi-machine power system Sreenivas Uravakonda 1 , Vijaya Kumar Mallapu 2 , Venkateswara Reddy Annapu Reddy 3 1 Department of Electrical and Electronics Engineering, Faculty of Engineering, Srinivasa Ramanujan Institute of Technology, Rotarypuram, Jawaharlal Nehru Technological University, Anantapur, India 2 Department of Electrical and Electronics Engineering, Faculty of Engineering, Jawaharlal Nehru Technological University, Anantapur, India 3 Department of Electrical and Electronics Engineering, Faculty of Engineering, Sai Rajeswari Institute of Technology, Proddatur, Jawaharlal Nehru Technological University, Anantapur, India Article Info ABSTRACT Article history: Received Jun 2, 2021 Revised Nov 24, 2021 Accepted Nov 27, 2021 In a multi-machine environment, the inter-area low-frequency oscillations induced due to small perturbation(s) has a significant adverse effect on the maximum limit of power transfer capacity of power system. Conventionally, to address this issue, power systems were equipped with lead-lag power system stabilizers (CPSS) for damping oscillations of low-frequency. In recent years the research was directed towards optimal control theory to design an optimal linear-quadratic-regultor (LQR) for stabilizing power system against the small perturbation(s). The optimal control theory provides a systematic way to design an optimal LQR with sufficient stability margins. Hence, LQR provides an improved level of performance than CPSS over broad-range of operating conditions. The process of designing of optimal LQR involves optimization of associated state (Q) and control (R) weights. This paper presents an analytical approach (AA) to design an optimal LQR by deriving algebraic equations for evaluating optimal elements for weight matrix ‘Q’. The performance of the proposed LQR is studied on an IEEE test system comprising 4-generators and 10-busbars. Keywords: Analytical approach Low-frequency oscillations LQR Optimal control theory Power system stabilizer This is an open access article under the CC BY-SA license. Corresponding Author: Sreenivas Uravakonda Department of Electrical and Electronics Engineering, Faculty of Engineering Srinivasa Ramanujan Institute of Technology, Rotarypuram, Jawaharlal Nehru Technological University Anantapur, Ananthapuramu, Andhra Pradesh, India Email: uravakonda.sreenivas@gmail.com 1. INTRODUCTION To enhance the damping performance of an electrical power system against small disturbance(s), an excitation-based power system stabilizer (CPSS) is extensively used around the world. Although the CPSSs have been used widely for satisfactorily damping local-mode low-frequency oscillations, the outcome of CPSS may not be the best possible because of the intuitive nature of the tuning process and restrictive assumptions made. Later, the research was directed towards optimal control theory to develop an optimal state-variable feedback gain controller i.e. linear-quadratic-regultor (LQR) for stabilizing power systems against small perturbation(s). Consequently, reports [1]-[10] have appeared in the literature concerning the application of optimal LQR for stabilizing power systems. In the referred papers [1]-[10], the design of LQR is based on the following sequential process: i) The control (R) and state (Q) weights are chosen as diagonal matrices; ii) The state weighing matrix Q is assigned numerical values arbitrarily by an iterative procedure; iii) Optimal LQR is determined; and