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Dissipativity-Based Distributed Control and Communication Topology Co-Design for DC Microgrids with ZIP Loads

Mohammad Javad Najafirad, Shirantha Welikala

TL;DR

The paper addresses voltage regulation and current sharing in DC microgrids with ZIP loads, where CPLs introduce destabilizing negative impedance effects. It develops a dissipativity-based, droop-free, hierarchical control and topology co-design that models the microgrid as a networked error system and optimizes controller gains and the communication topology via LMIs. The key contributions include a sector-bounded CPL handling framework, a one-shot local-global co-design methodology, and necessary conditions to ensure global dissipativity, enabling sparse yet robust interconnections. Simulation on a 4-DG islanded DC MG demonstrates improved voltage regulation and current sharing, with CPL robustness and favorable comparisons to traditional droop-based approaches.

Abstract

This paper presents a novel dissipativity-based distributed droop-free control and communication topology co-design approach for voltage regulation and current sharing in DC microgrids (DC MGs) with generic ``ZIP'' (constant impedance (Z), current (I) and power (P)) loads. While ZIP loads accurately capture the varied nature of the consumer loads, its constant power load (CPL) component is particularly challenging (and destabilizing) due to its non-linear form. Moreover, ensuring simultaneous voltage regulation and current sharing and co-designing controllers and topology are also challenging when designing control solutions for DC MGs. To address these three challenges, we model the DC MG as a networked system comprised of distributed generators (DGs), ZIP loads, and lines interconnected according to a static interconnection matrix. Next, we equip each DG with a local controller and a distributed global controller (over an arbitrary topology) to derive the error dynamic model of the DC MG as a networked ``error'' system, including disturbance inputs and performance outputs. Subsequently, to co-design the controllers and the topology ensuring robust (dissipative) voltage regulation and current sharing performance, we use the dissipativity and sector boundedness properties of the involved subsystems and formulate Linear Matrix Inequality (LMI) problems to be solved locally and globally. To support the feasibility of the global LMI problem, we identify and embed several crucial necessary conditions in the corresponding local LMI problems, thus providing a one-shot approach to solve the LMI problems. Overall, the proposed approach in this paper provides a unified framework for designing DC MGs. The effectiveness of the proposed solution was verified by simulating an islanded DC MG under different scenarios, demonstrating superior performance compared to traditional control approaches.

Dissipativity-Based Distributed Control and Communication Topology Co-Design for DC Microgrids with ZIP Loads

TL;DR

The paper addresses voltage regulation and current sharing in DC microgrids with ZIP loads, where CPLs introduce destabilizing negative impedance effects. It develops a dissipativity-based, droop-free, hierarchical control and topology co-design that models the microgrid as a networked error system and optimizes controller gains and the communication topology via LMIs. The key contributions include a sector-bounded CPL handling framework, a one-shot local-global co-design methodology, and necessary conditions to ensure global dissipativity, enabling sparse yet robust interconnections. Simulation on a 4-DG islanded DC MG demonstrates improved voltage regulation and current sharing, with CPL robustness and favorable comparisons to traditional droop-based approaches.

Abstract

This paper presents a novel dissipativity-based distributed droop-free control and communication topology co-design approach for voltage regulation and current sharing in DC microgrids (DC MGs) with generic ``ZIP'' (constant impedance (Z), current (I) and power (P)) loads. While ZIP loads accurately capture the varied nature of the consumer loads, its constant power load (CPL) component is particularly challenging (and destabilizing) due to its non-linear form. Moreover, ensuring simultaneous voltage regulation and current sharing and co-designing controllers and topology are also challenging when designing control solutions for DC MGs. To address these three challenges, we model the DC MG as a networked system comprised of distributed generators (DGs), ZIP loads, and lines interconnected according to a static interconnection matrix. Next, we equip each DG with a local controller and a distributed global controller (over an arbitrary topology) to derive the error dynamic model of the DC MG as a networked ``error'' system, including disturbance inputs and performance outputs. Subsequently, to co-design the controllers and the topology ensuring robust (dissipative) voltage regulation and current sharing performance, we use the dissipativity and sector boundedness properties of the involved subsystems and formulate Linear Matrix Inequality (LMI) problems to be solved locally and globally. To support the feasibility of the global LMI problem, we identify and embed several crucial necessary conditions in the corresponding local LMI problems, thus providing a one-shot approach to solve the LMI problems. Overall, the proposed approach in this paper provides a unified framework for designing DC MGs. The effectiveness of the proposed solution was verified by simulating an islanded DC MG under different scenarios, demonstrating superior performance compared to traditional control approaches.

Paper Structure

This paper contains 27 sections, 16 theorems, 130 equations, 8 figures.

Table of Contents

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

Key Result

Proposition 1

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

Figures (8)

  • Figure 1: Communication network impact on DC MG: (a) performance metrics versus link count and (b) network structure.
  • 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.
  • ...and 3 more figures

Theorems & Definitions (37)

  • Definition 1
  • Remark 1
  • Proposition 1
  • Remark 2
  • Remark 3
  • Proposition 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • ...and 27 more