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An integrated design of robust decentralized observer and controller for load frequency control

Xianxian Zhao, Jianglin Lan

TL;DR

The paper addresses decentralized load frequency control for interconnected multi-area power systems by introducing an integrated off-line design that co-creates decentralized observers and full-state feedback controllers using $H_\infty$ optimization formulated as a single-step $LMI$, explicitly incorporating inter-area interactions and bidirectional observer-controller effects. It further enhances transient performance through an $LMI$-based regional eigenvalue assignment in vertical strip regions, ensuring robust stability while constraining eigenvalue placement. The main contributions are the integrated design framework with off-line computation of $K_i$ and $L_{1i}$, the treatment of area-interactions as uncertainty, and the combination with eigenvalue assignment to improve time-domain performance. A three-area power system validates the approach, showing superior damping and faster settling compared with conventional decentralized designs under the same simulation conditions, while preserving complete decentralization in implementation. The results suggest the method is scalable and robust for large-scale multi-area systems with strong interconnections.

Abstract

This paper focuses on designing completely decentralized load frequency control (LFC) for multi-area power systems to achieve global optimized performance. To this end, a new concept of integrated design is introduced for designing the decentralized LFC observers and controllers simultaneously off-line, by taking into account of the interactions between areas and the bidirectional effects between the local observer and controller in each area. The integrated design in this paper is realized via $H_\infty$ optimization with a single-step linear matrix inequality (LMI) formulation. The LMI regional eigenvalue assignment technique is further incorporated with $H_\infty$ optimization to improve the closed-loop system transient performance. A three-area power system is simulated to validate the superiority of the proposed integrated design over the conventional decentralized designs.

An integrated design of robust decentralized observer and controller for load frequency control

TL;DR

The paper addresses decentralized load frequency control for interconnected multi-area power systems by introducing an integrated off-line design that co-creates decentralized observers and full-state feedback controllers using optimization formulated as a single-step , explicitly incorporating inter-area interactions and bidirectional observer-controller effects. It further enhances transient performance through an -based regional eigenvalue assignment in vertical strip regions, ensuring robust stability while constraining eigenvalue placement. The main contributions are the integrated design framework with off-line computation of and , the treatment of area-interactions as uncertainty, and the combination with eigenvalue assignment to improve time-domain performance. A three-area power system validates the approach, showing superior damping and faster settling compared with conventional decentralized designs under the same simulation conditions, while preserving complete decentralization in implementation. The results suggest the method is scalable and robust for large-scale multi-area systems with strong interconnections.

Abstract

This paper focuses on designing completely decentralized load frequency control (LFC) for multi-area power systems to achieve global optimized performance. To this end, a new concept of integrated design is introduced for designing the decentralized LFC observers and controllers simultaneously off-line, by taking into account of the interactions between areas and the bidirectional effects between the local observer and controller in each area. The integrated design in this paper is realized via optimization with a single-step linear matrix inequality (LMI) formulation. The LMI regional eigenvalue assignment technique is further incorporated with optimization to improve the closed-loop system transient performance. A three-area power system is simulated to validate the superiority of the proposed integrated design over the conventional decentralized designs.
Paper Structure (10 sections, 4 theorems, 31 equations, 8 figures, 1 table)

This paper contains 10 sections, 4 theorems, 31 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Multi-area power system model
  3. Integrated design of decentralized observer and controller
  4. Observer and controller structure
  5. Robust performance analysis and gains determination
  6. Time response improvement by eigenvalue assignment
  7. Simulation results
  8. Case 1: Without eigenvalue assignment
  9. Case 2: With eigenvalue assignment
  10. Conclusion

Key Result

Theorem 1

Given positive scalars $\gamma$ and $\varepsilon_1$, the composite closed-loop system (closed-sys2) is stable with $H_\infty$ performance $\| G_{z_c d} \|_{\infty} < \gamma$, if there exist symmetric positive definite matrices $P \in \mathbb{R}^{n \times n}$ and $Q \in \mathbb{R}^{n \times n}$, and where $\Pi_{1,1} = \mathrm{He} \left[ P (A - B K) + P \Delta A \right] + \varepsilon_1^{-1} \Delta

Figures (8)

  • Figure 1: Dynamic model of the $i$th area in a $\mathrm{N}$-area LFC scheme
  • Figure 2: Structure of the three-area power system
  • Figure 3: Eigenvalues of the control systems and observers using the integrated or separated strategies: Case 1
  • Figure 4: Frequency deviation: Case 1
  • Figure 5: Tie-line power flow deviation: Case 1
  • ...and 3 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Proof 1
  • Theorem 2
  • Proof 2
  • Lemma 1
  • Theorem 3
  • Proof 3