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State-Derivative Feedback Control for Damping Low-Frequency Oscillations in Bulk Power Systems

MST Rumi Akter, Anamitra Pal, Rajasekhar Anguluri

TL;DR

Low-frequency oscillations in bulk power systems with high renewable penetration are challenging to damp. The paper introduces a state-derivative feedback (SDF) damping controller that uses both area frequency and RoCoF to enhance damping and accelerate frequency recovery, enabling HVDC and energy storage to stabilize the grid. The authors show that, under standard assumptions, SDF can replicate state-feedback performance via the transformation $K_n = K_s (A - B K_s)^{-1}$ and $N_n = (I + K_n B) N_s$, while using readily measurable derivatives. They validate SDF on two- and three-area models against a frequency-difference scheme, demonstrating improved damping of intra-area modes and comparable inter-area damping with realistic noise and disturbances, suggesting SDF as a practical PMU-based damping strategy for power-electronics-rich grids.

Abstract

Low-frequency oscillations remain a major challenge in bulk power systems with high renewable penetration, long lines, and large loads. Existing damping strategies based on power modulation of high voltage DC (HVDC) or energy storage, are often limited by fixed control architectures, leaving some modes poorly damped. This paper introduces a state-derivative feedback (SDF) damping controller that uses both frequency and its rate of change as feedback signals. Incorporating state derivatives enhances modal damping and accelerates frequency recovery, enabling HVDC and energy storage to effectively stabilize the grid. We evaluate the SDF controller on two- and three-area systems and compare performance with a frequency difference-based damping scheme. Results show that the SDF control reproduces state-feedback performance while providing good damping of both inter- and intra-area oscillations compared to the frequency-difference method, highlighting its potential as a practical solution for stabilizing power-electronics-rich grids.

State-Derivative Feedback Control for Damping Low-Frequency Oscillations in Bulk Power Systems

TL;DR

Low-frequency oscillations in bulk power systems with high renewable penetration are challenging to damp. The paper introduces a state-derivative feedback (SDF) damping controller that uses both area frequency and RoCoF to enhance damping and accelerate frequency recovery, enabling HVDC and energy storage to stabilize the grid. The authors show that, under standard assumptions, SDF can replicate state-feedback performance via the transformation and , while using readily measurable derivatives. They validate SDF on two- and three-area models against a frequency-difference scheme, demonstrating improved damping of intra-area modes and comparable inter-area damping with realistic noise and disturbances, suggesting SDF as a practical PMU-based damping strategy for power-electronics-rich grids.

Abstract

Low-frequency oscillations remain a major challenge in bulk power systems with high renewable penetration, long lines, and large loads. Existing damping strategies based on power modulation of high voltage DC (HVDC) or energy storage, are often limited by fixed control architectures, leaving some modes poorly damped. This paper introduces a state-derivative feedback (SDF) damping controller that uses both frequency and its rate of change as feedback signals. Incorporating state derivatives enhances modal damping and accelerates frequency recovery, enabling HVDC and energy storage to effectively stabilize the grid. We evaluate the SDF controller on two- and three-area systems and compare performance with a frequency difference-based damping scheme. Results show that the SDF control reproduces state-feedback performance while providing good damping of both inter- and intra-area oscillations compared to the frequency-difference method, highlighting its potential as a practical solution for stabilizing power-electronics-rich grids.

Paper Structure

This paper contains 9 sections, 1 theorem, 9 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Setup and Preliminaries
  3. Primer on State-Derivative Feedback Control
  4. SDF Control for Oscillation Damping
  5. Simulation Results and Discussion
  6. Small Load Disturbance
  7. Fault Disturbance
  8. Data Center Load Fluctuation
  9. Conclusion

Key Result

Proposition 3

Consider the system matrix $A$ in eq: MMPS with non-singular $M$. Then $A$ is non-singular iff $T$ is non-singular.

Figures (6)

  • Figure 1: Damping controller in neely2013benefits vs. the proposed SDF control: Two power-system areas are connected by a tie-line interconnection, which may be an HVDC transmission link or equipped with an energy storage device. The damping controller in neely2013benefits regulates the source or sink power ($u$) in each area proportional to the frequency difference $\Delta\omega_1 - \Delta\omega_2$. In contrast, the SDF control regulates this power based on the individual frequencies $(\Delta\omega_1, \Delta\omega_2)$ and their derivatives $(\Delta\dot{\omega}_1, \Delta\dot{\omega}_2)$, providing greater flexibility through derivative terms and without restricting the control actuation via difference quantities.
  • Figure 2: Control inputs for the two-area system under SF and SDF.
  • Figure 3: System responses for $1\%$ load increase in Area 1. In the legend, A$\mathrm{j}$ refers to the $\mathrm{j}$-th area.
  • Figure 4: System responses under measurement noise consistent with PMU accuracy limits.
  • Figure 5: System responses to a short-duration fault in Area 1
  • ...and 1 more figures

Theorems & Definitions (4)

  • proof
  • Proposition 3
  • proof
  • Example 1