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Unified Control of Voltage, Frequency and Angle in Electrical Power Systems: A Passivity and Negative-Imaginary based Approach

Yijun Chen, Kanghong Shi, Ian R. Petersen, Elizabeth L. Ratnam

TL;DR

The paper tackles unified control of voltage, frequency, and rotor angle in power networks by formulating an output-consensus problem within a passivity and negative-imaginary framework. It develops distributed, phasor-feedback controllers using co-located large-scale batteries to separately regulate real and reactive power, decoupling angle/frequency dynamics from voltage magnitude dynamics. Theoretical results establish local output consensus for networked passive and NI systems under appropriate interconnections, and these are instantiated in a power-system setting with a decoupled angle loop (NI/OSNI) and a decoupled voltage loop (passive/OS). Numerical simulations on a four-area network validate frequency synchronization, angle-difference preservation, and voltage regulation, demonstrating robustness and practical viability of the approach for grid modernization. The work lays groundwork for fully distributed, measurement-driven control of voltage, frequency, and angle using energy storage assets, with future directions including actuator saturation and implementation challenges.

Abstract

This paper proposes a unified methodology for voltage regulation, frequency synchronization, and rotor angle control in power transmission systems considering a one-axis generator model with time-varying voltages. First, we formulate an output consensus problem with a passivity and negative-imaginary (NI) based control framework. We establish output consensus results for both networked passive systems and networked NI systems. Next, we apply the output consensus problem by controlling large-scale batteries co-located with synchronous generators -- using real-time voltage phasor measurements. By controlling the battery storage systems so as to dispatch real and reactive power, we enable simultaneous control of voltage, frequency, and power angle differences across a transmission network. Validation through numerical simulations on a four-area transmission network confirms the robustness of our unified control framework.

Unified Control of Voltage, Frequency and Angle in Electrical Power Systems: A Passivity and Negative-Imaginary based Approach

TL;DR

The paper tackles unified control of voltage, frequency, and rotor angle in power networks by formulating an output-consensus problem within a passivity and negative-imaginary framework. It develops distributed, phasor-feedback controllers using co-located large-scale batteries to separately regulate real and reactive power, decoupling angle/frequency dynamics from voltage magnitude dynamics. Theoretical results establish local output consensus for networked passive and NI systems under appropriate interconnections, and these are instantiated in a power-system setting with a decoupled angle loop (NI/OSNI) and a decoupled voltage loop (passive/OS). Numerical simulations on a four-area network validate frequency synchronization, angle-difference preservation, and voltage regulation, demonstrating robustness and practical viability of the approach for grid modernization. The work lays groundwork for fully distributed, measurement-driven control of voltage, frequency, and angle using energy storage assets, with future directions including actuator saturation and implementation challenges.

Abstract

This paper proposes a unified methodology for voltage regulation, frequency synchronization, and rotor angle control in power transmission systems considering a one-axis generator model with time-varying voltages. First, we formulate an output consensus problem with a passivity and negative-imaginary (NI) based control framework. We establish output consensus results for both networked passive systems and networked NI systems. Next, we apply the output consensus problem by controlling large-scale batteries co-located with synchronous generators -- using real-time voltage phasor measurements. By controlling the battery storage systems so as to dispatch real and reactive power, we enable simultaneous control of voltage, frequency, and power angle differences across a transmission network. Validation through numerical simulations on a four-area transmission network confirms the robustness of our unified control framework.
Paper Structure (16 sections, 4 theorems, 25 equations, 7 figures, 3 tables)

This paper contains 16 sections, 4 theorems, 25 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Passive Systems
  4. Negative-Imaginary Systems
  5. Output Consensus of Networked Systems
  6. Settings for Networked Systems
  7. Main Results
  8. Output Consensus for Networked Passive Systems
  9. Output Consensus for Networked NI Systems
  10. Application to Power Transmission Systems
  11. One-axis Generator Model
  12. Feedback Decoupling and Linearization
  13. Decoupled Angle Dynamics
  14. Decoupled voltage dynamics
  15. Simulations
  16. ...and 1 more sections

Key Result

Theorem 1

Consider passive node plants $H_{pi}, i \in \mathcal{V}$. Also consider output strictly passive edge controllers $H_{cl}, l \in \mathcal{L}$. Suppose Assumptions apt:g, apt:equilibrium, apt:state_output_consistency, and apt:input_state_consistency hold for all node plants $H_{pi}, i \in \mathcal{V}$

Figures (7)

  • Figure 1: The positive (negative) feedback interconnection of nonlinear plants $\mathcal{H}_{p}$ and nonlinear edge controllers $\mathcal{H}_{c}$ based on the underlying network, where the feedback sign is '$+$' in red ('$-$' in blue).
  • Figure 2: The feedback control framework, where the angle dynamics and the voltage dynamics can be decoupled.
  • Figure 3: The control architecture.
  • Figure 4: A four area equivalent network, where A$_{i}, i \in \mathcal{V}$ represents area $i$, and $B_{ij}, (i,j) \in \mathcal{E}$ represents the susceptance of the transmission line $(i,j)$trip2016internalnabavi2013topology.
  • Figure 5: Frequencies of generator buses.
  • ...and 2 more figures

Theorems & Definitions (14)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5: Output Consensus
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Remark 3
  • ...and 4 more