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A mixed Hinfty-Passivity approach for Leveraging District Heating Systems as Frequency Ancillary Service in Electric Power Systems

Xinyi Yi, Ioannis Lestas

Abstract

This paper introduces a mixed H-infinity-passivity framework that enables district heating systems (DHSs) with heat pumps to support electric-grid frequency regulation. The analysis illustrates how the DHS regulator influences coupled electro-thermal frequency dynamics and provides LMI conditions for efficient controller design. We also present a disturbance-independent temperature regulator that ensures stability and robustness against heat-demand uncertainty. Simulations demonstrate improved frequency-control dynamics in the electrical power grid while maintaining good thermal performance in the DHS.

A mixed Hinfty-Passivity approach for Leveraging District Heating Systems as Frequency Ancillary Service in Electric Power Systems

Abstract

This paper introduces a mixed H-infinity-passivity framework that enables district heating systems (DHSs) with heat pumps to support electric-grid frequency regulation. The analysis illustrates how the DHS regulator influences coupled electro-thermal frequency dynamics and provides LMI conditions for efficient controller design. We also present a disturbance-independent temperature regulator that ensures stability and robustness against heat-demand uncertainty. Simulations demonstrate improved frequency-control dynamics in the electrical power grid while maintaining good thermal performance in the DHS.
Paper Structure (24 sections, 7 theorems, 25 equations, 3 figures, 1 table)

This paper contains 24 sections, 7 theorems, 25 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model Formulation
  3. Heat pump
  4. Electric power system
  5. Frequency dynamic model of electric buses
  6. Secondary frequency control
  7. District heating system
  8. Temperature dynamics
  9. Energy-sharing steady-state objectives
  10. Augmented DHS
  11. PASSIVITY-BASED FREQUENCY AND TEMPERATURE CONTROL
  12. Stability and optimality of the CHP system
  13. Mixed $H_\infty$/Passivity Controller Design
  14. Passivity-based controller design
  15. $\mathcal{H}_\infty$ frequency–shaping filter
  16. ...and 9 more sections

Key Result

Lemma 1

Under Assumption 1, for any constant disturbances $\boldsymbol{\bar{P}^{L}}$ and $\boldsymbol{\bar{p}^{H}}$, the EPS model with the AGC controller gen_dyn-eq:agc admits a unique equilibrium $(\boldsymbol{x_\theta^*}, \boldsymbol{\theta^*}, \boldsymbol{u^*}, \boldsymbol{\omega^*}, \boldsymbol{P^{G*}}

Figures (3)

  • Figure 1: DHS with differenent types of disturbances.
  • Figure 2: Frequency response $\boldsymbol{\omega^{HP}\!\to\!p^H}$.
  • Figure 3: CHP system operation with different $\gamma^E$ and $\gamma^H$.

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Theorem 1
  • Lemma 6