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Fully Distributed Adaptive Consensus Approach for Economic Dispatch Problem

Arnab Pal, Suman Singha Roy, Asim Kumar Naskar

Abstract

This research presents a novel approach to solving the economic load dispatch (ELD) problem in smart grid systems by leveraging a multi-agent distributed consensus strategy. The core idea revolves around achieving agreement among generators on their incremental cost values, thereby enabling an optimal allocation of power generation. To enhance convergence and robustness, the study introduces an adaptive coupling weight mechanism within a fully decentralized consensus framework, carefully designed with appropriate initial settings for incremental costs. The proposed distributed control protocol is versatile it functions effectively in both constrained and unconstrained generator capacity scenarios. Importantly, the methodology ensures that total power generation continuously matches dynamic load demands throughout the dispatch process, maintaining system-wide balance. To accommodate fluctuating and time varying load profiles, a dummy node is incorporated into the network architecture, acting as a flexible proxy for real time demand changes. The resilience of the method is further evaluated under communication disruptions, specifically by analyzing generator link failures through a switching network topology. Stability of the system is rigorously established using a Lyapunov-based analysis, assuming an undirected and connected communication graph among agents. To validate the practical efficacy of the proposed technique, comprehensive simulations are conducted on the IEEE 30 bus test system within the MATLAB environment, confirming its accuracy, adaptability, and computational efficiency in realistic smart grid conditions.

Fully Distributed Adaptive Consensus Approach for Economic Dispatch Problem

Abstract

This research presents a novel approach to solving the economic load dispatch (ELD) problem in smart grid systems by leveraging a multi-agent distributed consensus strategy. The core idea revolves around achieving agreement among generators on their incremental cost values, thereby enabling an optimal allocation of power generation. To enhance convergence and robustness, the study introduces an adaptive coupling weight mechanism within a fully decentralized consensus framework, carefully designed with appropriate initial settings for incremental costs. The proposed distributed control protocol is versatile it functions effectively in both constrained and unconstrained generator capacity scenarios. Importantly, the methodology ensures that total power generation continuously matches dynamic load demands throughout the dispatch process, maintaining system-wide balance. To accommodate fluctuating and time varying load profiles, a dummy node is incorporated into the network architecture, acting as a flexible proxy for real time demand changes. The resilience of the method is further evaluated under communication disruptions, specifically by analyzing generator link failures through a switching network topology. Stability of the system is rigorously established using a Lyapunov-based analysis, assuming an undirected and connected communication graph among agents. To validate the practical efficacy of the proposed technique, comprehensive simulations are conducted on the IEEE 30 bus test system within the MATLAB environment, confirming its accuracy, adaptability, and computational efficiency in realistic smart grid conditions.
Paper Structure (20 sections, 4 theorems, 42 equations, 15 figures, 1 table)

This paper contains 20 sections, 4 theorems, 42 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph Theory
  4. Consensus of Multi-agent system
  5. Representation of Power System Network as Graph Topology
  6. Problem formulation
  7. Solution to power dispatch problem
  8. Adaptive consensus protocol for economic dispatch
  9. Optimal Power Dispatch With Capacity Limitations
  10. Optimal Power Dispatch with Constant Demand
  11. Problem Formulation
  12. Distributed consensus Protocol with the capacity limit for optimal power dispatch
  13. Optimal power dispatch with Time-Varying Demand
  14. Optimum Power Dispatch with Generator Communication Link Failure
  15. Simulation Examples
  16. ...and 5 more sections

Key Result

Theorem 1

Under fixed undirected network topology among the generating nodes, the adaptive consensus method described by where $\beta_{ij}=\beta_{ji}$ are positive scalars, $a_{ij}(t)$ is the entries of the adjacency matrix and can maintain stability when applied to solve the economic load dispatch problem expressed by Conditions 1 and 2.

Figures (15)

  • Figure 1: Combined view of the IEEE-30 Bus System and its Network Topology
  • Figure 2: Network Topology
  • Figure 3: Incremental cost consensus
  • Figure 4: Adaptive weights $a_{ij}, i,j=1,2,...,N$
  • Figure 5: Output powers
  • ...and 10 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Remark 1
  • Theorem 2
  • Theorem 3
  • Remark 2
  • Theorem 4
  • Remark 3