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Damping Enhancement for SMIB Power System Equipped with LQR Tuned via Analytical Approach

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Abstract

Among several aspects of stability of synchronous machine operation, an important aspect is the mode of ‘small perturbation stability’ referred to as steady-state, 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 proposed analytical method has been tested in MATLAB/Simulink® environment.

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Abbreviations

E b :

Infinite-bus voltage

V s :

Secondary voltage of step-up transformer

V t :

Generator terminal voltage

\(E_{q}^{\prime}\) :

Equivalent induced voltage along q-axis

P s :

Active power at step-up transformer secondary bus

Q s :

Reactive power at step-up transformer secondary bus

P t :

Active power at generator terminal

Q t :

Reactive power at generator terminal

P g :

Generated active power

Q g :

Generated reactive power

θ s :

Angle between Vs and Eb

θ t :

Angle of terminal voltage Vt

δ :

Rotor angle between Eb and q-axis

δ s :

Rotor angle between Vs and q-axis

R L :

Equivalent resistance of transmission system

X L :

Equivalent reactance of transmission system

R t :

Resistance of step-up transformer

X t :

Reactance of step-up transformer

R e :

Equivalent resistance of SMIB system

X e :

Equivalent reactance of SMIB system

\(x_{d}^{\prime}\) :

d-Axis transient reactance of generator

H :

Inertia constant

D :

Damping torque coefficient

\(\omega_{B}\) :

Base angular frequency

T m :

Mechanical torque input

T e :

Electrical torque output

T D :

Damping torque

K E :

Exciter gain

T E :

Exciter time constant

\(T_{do}^{\prime}\) :

Open-circuit transient time constant

T 1 :

Feed-forward time constant of phase compensator of CPSS

T 2 :

Feed-backward time constant of phase compensator of CPSS

T w :

Time constant of washout block of CPSS

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, SSSISE, JNT University, Anantapur, Ananthapuramu, Andhra Pradesh, 515001, India

    Sreenivas Uravakonda

  2. Department of Electrical and Electronics Engineering, CEA, JNT University, Anantapur, Ananthapuramu, Andhra Pradesh, 515002, India

    Vijaya Kumar Mallapu

  3. Department of Electrical and Electronics Engineering, SVIST, JNT University, Anantapur, Kadapa, Andhra Pradesh, 516001, India

    Venkateswara Reddy Annapu Reddy

Authors
  1. Sreenivas Uravakonda
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  2. Vijaya Kumar Mallapu
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  3. Venkateswara Reddy Annapu Reddy
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Correspondence to Sreenivas Uravakonda.

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Uravakonda, S., Mallapu, V.K. & Annapu Reddy, V.R. Damping Enhancement for SMIB Power System Equipped with LQR Tuned via Analytical Approach. J. Inst. Eng. India Ser. B 101, 541–551 (2020). https://doi.org/10.1007/s40031-020-00484-3

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