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Dissipativity-Based Distributed Control and Communication Topology Co-Design for Nonlinear DC Microgrids

Mohammad Javad Najafirad, Shirantha Welikala

Abstract

This paper presents a dissipativity-based distributed droop-free control and communication topology co-design framework for voltage regulation and current sharing in DC microgrids (MGs), where constant-power loads (CPLs) and voltage-source converter (VSC) input saturation introduce significant nonlinearities. In particular, CPLs introduce an inherently destabilizing nonlinearity, while VSC input saturation imposes hard amplitude constraints on applicable control input at each distributed generator (DG), collectively making the DC MG control system design extremely challenging. To this end, the DC MG is modeled as a networked system of DGs, transmission lines, and loads coupled through a static interconnection matrix. Each DG is equipped with a local PI-based controller with an anti-windup compensator and a distributed consensus-based global controller, from which a nonlinear networked error dynamics model is derived. The CPL nonlinearity is characterized via sector-boundedness with the S-procedure applied directly to yield tight LMI conditions, while the VSC input saturation is handled via a dead-zone decomposition and sector-boundedness, with both nonlinearities simultaneously absorbed into the dissipativity analysis. Both nonlinearities are simultaneously absorbed into the dissipativity analysis using the S-procedure. Subsequently, local controller gains and passivity indices, and distributed controller gains and the communication topology are co-designed by solving a sequence of local and global Linear Matrix Inequality (LMI) problems, enabling a one-shot co-design process that avoids iterative procedures. The effectiveness of the proposed framework is validated through simulation of an islanded DC MG under multiple operating scenarios, demonstrating robust performance superior to conventional control approaches.

Dissipativity-Based Distributed Control and Communication Topology Co-Design for Nonlinear DC Microgrids

Abstract

This paper presents a dissipativity-based distributed droop-free control and communication topology co-design framework for voltage regulation and current sharing in DC microgrids (MGs), where constant-power loads (CPLs) and voltage-source converter (VSC) input saturation introduce significant nonlinearities. In particular, CPLs introduce an inherently destabilizing nonlinearity, while VSC input saturation imposes hard amplitude constraints on applicable control input at each distributed generator (DG), collectively making the DC MG control system design extremely challenging. To this end, the DC MG is modeled as a networked system of DGs, transmission lines, and loads coupled through a static interconnection matrix. Each DG is equipped with a local PI-based controller with an anti-windup compensator and a distributed consensus-based global controller, from which a nonlinear networked error dynamics model is derived. The CPL nonlinearity is characterized via sector-boundedness with the S-procedure applied directly to yield tight LMI conditions, while the VSC input saturation is handled via a dead-zone decomposition and sector-boundedness, with both nonlinearities simultaneously absorbed into the dissipativity analysis. Both nonlinearities are simultaneously absorbed into the dissipativity analysis using the S-procedure. Subsequently, local controller gains and passivity indices, and distributed controller gains and the communication topology are co-designed by solving a sequence of local and global Linear Matrix Inequality (LMI) problems, enabling a one-shot co-design process that avoids iterative procedures. The effectiveness of the proposed framework is validated through simulation of an islanded DC MG under multiple operating scenarios, demonstrating robust performance superior to conventional control approaches.

Paper Structure

This paper contains 28 sections, 15 theorems, 111 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Dissipativity
  5. Networked Systems
  6. Linear Algebraic Preliminaries
  7. Problem Formulation
  8. DC MG Physical Interconnection Topology
  9. Dynamic Model of a Distributed Generator (DG)
  10. Dynamic Model of a Transmission Line
  11. Dynamic Model of a ZIP Load
  12. Nonlinearities in DC MGs
  13. Proposed Hierarchical Control Architecture
  14. Local Voltage Regulating Controller
  15. Distributed Global Controller
  16. ...and 13 more sections

Key Result

Proposition 1

welikala2023platoon The LTI system is $X$-dissipative if and only if there exists $P>0$ such that

Figures (5)

  • Figure 2: A generic networked system $\Sigma$.
  • Figure 3: The electrical schematic of DG-$i$, load-$i$, $i\in\mathbb{N}_N$, local controller, distributed global controller, and line-$l$, $l\in\mathbb{N}_L$.
  • Figure 4: DC MG dynamics as a networked system configuration.
  • Figure 5: DC MG error dynamics as a networked system with disturbance inputs and performance outputs.
  • Figure 6: Sector-bounded characterizations of (left) the CPL nonlinearity $g_i(\tilde{V}_i)$ bounded between slopes $\alpha_i$ and $\beta_i$, and (right) the dead-zone nonlinearity $\phi_i(u_i)$ bounded within the sector $[0, -1]$.

Theorems & Definitions (31)

  • Definition 1
  • Definition 2
  • Remark 1
  • Proposition 1
  • Proposition 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • ...and 21 more