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Distributed solution methods for MPC based energy management method of interconnected microgrids: Dual ascent vs ADMM

Viet Hoang Pham, Hyo-Sung Ahn

TL;DR

This work tackles MPC based energy management for networks of interconnected microgrids under forecast uncertainty. It develops two distributed solvers, a dual ascent gradient projection method and a proximal ADMM approach, enabling each microgrid to compute its own control actions using only local information and neighbor communication. The uncertainty is addressed via a chance constraint reformulation that yields deterministic bounds using the predicted mean and variance of demands and capacities. Numerical tests on a modified IEEE 30-bus network demonstrate convergence to the optimal solution with favorable scalability, highlighting the methods’ suitability for real time, distributed energy management in resilient microgrid architectures.

Abstract

This paper considers an optimal energy management problem for a network of interconnected microgrids. A model predictive control (MPC) approach is used to avoid capacity constraint violation and to cope with uncertainties of forecasted power demands. By employing a dual ascent method and a proximal alternative direction multiplier method (ADMM), respectively, two distributed methods are designed to allow every agent using only local information to determine its own optimal control decisions. The effectiveness of the proposed method is verified via numerical simulations.

Distributed solution methods for MPC based energy management method of interconnected microgrids: Dual ascent vs ADMM

TL;DR

This work tackles MPC based energy management for networks of interconnected microgrids under forecast uncertainty. It develops two distributed solvers, a dual ascent gradient projection method and a proximal ADMM approach, enabling each microgrid to compute its own control actions using only local information and neighbor communication. The uncertainty is addressed via a chance constraint reformulation that yields deterministic bounds using the predicted mean and variance of demands and capacities. Numerical tests on a modified IEEE 30-bus network demonstrate convergence to the optimal solution with favorable scalability, highlighting the methods’ suitability for real time, distributed energy management in resilient microgrid architectures.

Abstract

This paper considers an optimal energy management problem for a network of interconnected microgrids. A model predictive control (MPC) approach is used to avoid capacity constraint violation and to cope with uncertainties of forecasted power demands. By employing a dual ascent method and a proximal alternative direction multiplier method (ADMM), respectively, two distributed methods are designed to allow every agent using only local information to determine its own optimal control decisions. The effectiveness of the proposed method is verified via numerical simulations.
Paper Structure (19 sections, 8 theorems, 61 equations, 3 figures, 3 tables)

This paper contains 19 sections, 8 theorems, 61 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Notations
  3. MPC energy management problem
  4. Network of interconnected microgrids
  5. MPC approach
  6. Problem statement
  7. Reformulation for uncertain prediction
  8. Communication graph
  9. Distributed solution based on dual ascent method
  10. Compact form of MPC energy management problem
  11. Distributed solution method
  12. ADMM-based solution method
  13. Compact form of MPC energy management problem
  14. Distributed solution method
  15. Numerical simulations
  16. ...and 4 more sections

Key Result

Lemma 1

If Assumption aspt_4 is satisfied, we have

Figures (3)

  • Figure 1: A network of $5$ interconnected microgrids.
  • Figure 2: Test system with 10 generators.
  • Figure 3: Convergences of the estimated solutions to the precise optimal solutions under three distributed optimization methods.

Theorems & Definitions (10)

  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Proposition 1: Proposition 6.1.1 DimitriPBertsekas1999
  • Proposition 2: Proposition 5.3.1 DimitriPBertsekas1999
  • Proposition 3: Proposition 5.1.1 DimitriPBertsekas1999
  • Proposition 4