Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

DC Microgrids with Nested Nonlinear Distributed Control: Scalable Large-Signal Stability and Voltage Containment

Cornelia Skaga, Mahdieh S. Sadabadi, Gilbert Bergna-Diaz

TL;DR

This paper investigates a cyber-physical DC microgrid employing a nonlinear distributed consensus-based control scheme for coordinated integration and management of distributed generating units within an expandable framework that achieves proportional current sharing among all distributed generation units.

Abstract

This paper investigates a cyber-physical DC microgrid employing a nonlinear distributed consensus-based control scheme for coordinated integration and management of distributed generating units within an expandable framework. Relying on nested primary andsecondary control loops; a (distributed) outer-loop and a (decentralized) inner-loop, the controller achieves proportional current sharing among all distributed generation units, while dynamically operating within predefined voltage limits. A rigorous Lyapunov-based stability analysis establishes a scalable global exponential stability certificate under some tuning conditions and sufficient time-scale separation between the control loops, based on singular perturbation theory. An optimization-based tuning strategy is then formulated to identify and subsequently diminish unstable operating conditions. In turn, various practical tuning strategies are introduced to provide stable operations while facilitating near-optimal proportional current sharing. The effectiveness of the proposed control framework and tuning approaches are finally supported through time-domain simulations of a case-specific low-voltage DC microgrid.

DC Microgrids with Nested Nonlinear Distributed Control: Scalable Large-Signal Stability and Voltage Containment

TL;DR

This paper investigates a cyber-physical DC microgrid employing a nonlinear distributed consensus-based control scheme for coordinated integration and management of distributed generating units within an expandable framework that achieves proportional current sharing among all distributed generation units.

Abstract

This paper investigates a cyber-physical DC microgrid employing a nonlinear distributed consensus-based control scheme for coordinated integration and management of distributed generating units within an expandable framework. Relying on nested primary andsecondary control loops; a (distributed) outer-loop and a (decentralized) inner-loop, the controller achieves proportional current sharing among all distributed generation units, while dynamically operating within predefined voltage limits. A rigorous Lyapunov-based stability analysis establishes a scalable global exponential stability certificate under some tuning conditions and sufficient time-scale separation between the control loops, based on singular perturbation theory. An optimization-based tuning strategy is then formulated to identify and subsequently diminish unstable operating conditions. In turn, various practical tuning strategies are introduced to provide stable operations while facilitating near-optimal proportional current sharing. The effectiveness of the proposed control framework and tuning approaches are finally supported through time-domain simulations of a case-specific low-voltage DC microgrid.
Paper Structure (19 sections, 3 theorems, 29 equations, 8 figures, 2 tables)

This paper contains 19 sections, 3 theorems, 29 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Literature review and Research Gap
  3. Contributions
  4. System Modeling and Control Framework
  5. Nonlinear Nested Distributed Control Framework
  6. Dynamical Model of Closed-Loop DC Microgrid
  7. System Steady State and Stability
  8. Equilibrium Analysis
  9. Optimal Steady State Conditions
  10. Singular Perturbation Theory
  11. Lyapunov Stability Analysis
  12. Tuning Guidelines for Stability Guarantees
  13. Decentralized Tuning Strategies for G.E.S.
  14. Preserving the Time-Scale Separation
  15. Case Studies
  16. ...and 4 more sections

Key Result

Theorem 1

(Singular Perturbed Problem) Consider the closed loop dynamics in complete_sys_compact, and let where $\mathrm{h}(v)=\mathrm{bcol}\{\mathrm{h}^{I^\mathcal{G}}_i(v), \mathrm{h}_j^{I^\mathcal{E}}(v), \mathrm{h}^{V^\mathcal{N}}_k (v), \mathrm{h}^{\lambda}_i(v), \mathrm{h}^{\zeta}_i(v)\}, \forall i \in \mathcal{G}, \forall j \in \mathcal{E}, \forall k \in \mathcal{N}$ is the unique solution of $\v

Figures (8)

  • Figure 1: Cyber Physical DC Microgrid
  • Figure 2: Tuning Strategy for G.E.S. and Proportional Current Sharing
  • Figure 3: Case Specific Microgrid
  • Figure 4: Nonlinear Leakage Functions
  • Figure 5: Gashgorin Circle Theorem Plots: Base-case system (first row), tuned system with individual permanent leakage ($\mathcal{B}_v$) (second and third row); (a)-(h) center v.s. radius for each row in $\mathcal{Z}(v)$; (i)-(l) Geršgorin disc of each row in $\mathcal{Z}(v)$ for the worst case scenario
  • ...and 3 more figures

Theorems & Definitions (10)

  • Remark 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • proof
  • Remark 2
  • Remark 3
  • Remark 4