IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 04 | Apr-2013, Available @ http://www.ijret.org 724 A ROBUST DLQG CONTROLLER FOR DAMPING OF SUB - SYNCHRONOUS OSCILLATIONS IN A SERIES COMPENSATED POWER SYSTEM K.C. Sindhu Thampatty 1 , P. C. Reghu Raj 2 1 Associate Professor, Dept. of Electrical and Electronics Engg, Amrita Viswa Vidyapeetham, Coimbatore, Tamilnadu, 2 Prof & Head, Department of Computer Science and Engineering, Govt. Engineering College, Sreekrishnapuram, Palakkad, Kerala, kc_sindhu@yahoo.com pcreghu@gmail.com Abstract This paper investigates the use of Discrete Linear Quadratic Gaussian (DLQG) Compensator to damp sub synchronous oscillations in a Thyrisor Controlled Series Capacitor (TCSC) compensated power system. The study is conducted on IEEE First Benchmark Model (FBM) in which, TCSC is modelled as a discrete linear time-invariant modular unit in the synchronously rotating DQ reference frame. This modular TCSC is then integrated with the Linear Time Invariant (LTI) model of the rest of the system. The design of DLQG includes the design of a Kalman filter for full state estimation and a full state feedback for control. Since the order of the controller is as large as the order of the system considered here(27 states), the practical implementation of the controller is difficult. Hence by using Hankels norm approximation technique, the order of the controller is reduced from 27 to 15 without losing the significant system dynamics. The eigen analysis of the system shows that the use of DLQG can damp torsional oscillations as well as the swing mode oscillations simultaneously, which is practically difficult for a conventional sub-synchronous damping controller. The performance of the system with DLQG is appreciable for all operating conditions and it shows the robustness of the controller. Index Terms: Sub-Synchronous Resonance (SSR), Torsional Oscillations, Thyristor Controlled Series Capacitor (TCSC), Discrete Linear Quadratic Gaussian(DLQG)Compensator, Model Order Reduction (MOR). -----------------------------------------------------------------------***----------------------------------------------------------------------- 1. INTRODUCTION Series capacitors have been used extensively as an economical means to increase load carrying capability, control load sharing among parallel lines and enhance transient stability. However, capacitors in series with transmission lines may cause sub- synchronous resonance that can lead to turbine- generator shaft failure and electrical instability at oscillation frequencies lower than the normal system frequency [1]- [3]. Sub-synchronous resonance (SSR) has gained its name from the fact that the frequencies of interest happened to lie in a region below the synchronous frequency of the network. The phenomenon of SSR was brought to general attention in connection with the two damages that occurred to the turbine - generator shafts at the Mohave Generating station in southern Nevada in the United States of America in December of 1970 and October of 1971. These two failures were analyzed and found that the failures occurred in the shaft section between the generator and the exciter of the main generator collector was due to torsional fatigue [4]- [6]. Torsional problems are most frequently encountered in rotor systems with long shafts and large inertias constituting a weakly damped mechanical system. The normal subsynchronous frequency range is between 10 to 50 Hz where as the swing mode oscillations are between 0.7 Hz to 2 Hz. Therefore the simultaneous dampings of these oscillations are difficult with a conventional controller. Numerous papers are published on different approaches in sub-synchronous analysis and also the use of Flexible AC Transmission System (FACTS) devices to damp electromechanical oscillations [7]. Many methods [8]- [10] are proposed using series and shunt FACTS devices to improve the power system dynamic stability. To do the stability analysis, a perfect modelling of the power system is required. Various efforts have been made in the past few years to obtain a linearised state space models of TCSC [11], [12]. A modular model of TCSC is derived by Othman and Angquist [13], in which the TCSC model is derived independently and then interfaced with the rest of the system. Kabiri et al. [14] developed a discrete model with higher sampling rate (six samples per cycle), which is a sample- variant model. In this work, the IEEE First Benchmark model with the series compensation partly done by TCSC and partly by fixed capacitor is considered. A discrete linear time invariant state space model of TCSC is presented based on Poincare mapping technique [15]. The model is based on six