Damping Enhancement for SMIB Power System Equipped with LQR Tuned via Analytical Approach
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REVIEW PAPER
Damping Enhancement for SMIB Power System Equipped with LQR Tuned via Analytical Approach Sreenivas Uravakonda1 • Vijaya Kumar Mallapu2 • Venkateswara Reddy Annapu Reddy3
Received: 18 June 2019 / Accepted: 21 August 2020 Ó The Institution of Engineers (India) 2020
Abstract Among several aspects of stability of synchronous machine operation, an important aspect is the mode of ‘small perturbation stability’ referred to as steadystate, dynamic or conditional stability. Attention has been increasing on the effect of excitation control in damping small-frequency rotor oscillations which characterize the phenomena of dynamic stability. In particular, it has been found useful and practical to incorporate stabilizing signals derived from speed and/or terminal frequency and/or power superposed on the normal voltage error signal of automatic voltage regulators to provide an additional damping to these oscillations. Conventionally, the lead–lag power system stabilizer (CPSS) is employed to supplement stabilizing signal to normal voltage error signal for damping these rotor oscillations of small frequency typically ranges from 0.2 to 3.5 Hz. In recent years, researchers have been proposing linear quadratic regulator (LQR) to replace CPSS for damping these small-frequency rotor oscillations. In this paper, an ‘algebraic approach’ derived from the relationship between algebraic Riccati equation and Lagrange multiplier optimization technique is proposed to tune LQR. The performance of single-machine infinite-bus power system equipped with LQR tuned via the & Sreenivas Uravakonda [email protected] 1
Department of Electrical and Electronics Engineering, SSSISE, JNT University, Anantapur, Ananthapuramu, Andhra Pradesh 515001, India
2
Department of Electrical and Electronics Engineering, CEA, JNT University, Anantapur, Ananthapuramu, Andhra Pradesh 515002, India
3
Department of Electrical and Electronics Engineering, SVIST, JNT University, Anantapur, Kadapa, Andhra Pradesh 516001, India
proposed analytical method has been tested in MATLAB/ SimulinkÒ environment. Keywords LQR Analytical approach ARE Lagrange multiplier optimization technique List Eb Vs Vt Eq0 Ps Qs Pt Qt Pg Qg hs ht d ds RL XL Rt Xt Re Xe x0d H D xB Tm Te TD
of Symbols Infinite-bus voltage Secondary voltage of step-up transformer Generator terminal voltage Equivalent induced voltage along q-axis Active power at step-up transformer secondary bus Reactive power at step-up transformer secondary bus Active power at generator terminal Reactive power at generator terminal Generated active power Generated reactive power Angle between Vs and Eb Angle of terminal voltage Vt Rotor angle between Eb and q-axis Rotor angle between Vs and q-axis Equivalent resistance of transmission system Equivalent reactance of transmission system Resistance of step-up transformer Reactance of step-up transformer Equivalent resistance of SMIB system Equivalent reactance of SMIB system d-Axis transient reactance of generator Inertia constant Damping torque coe
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