[Paper Review] Optimal Power Management for Failure Mode of MVDC Microgrids in All-Electric Ships

Qimin Xu, Bo Yang+3 more|arXiv (Cornell University)|Dec 7, 2017

Maritime Transport Emissions and Efficiency17 references3 citations

TL;DR

This paper proposes an optimal power management framework for medium-voltage DC (MVDC) microgrids in all-electric ships during failure modes, integrating load shedding and network reconfiguration to ensure system stability and minimize operating costs. By convexifying non-convex constraints and using Benders decomposition with a low-complexity variant (LNBD), the method ensures feasibility and convergence, achieving up to 98.7% load restoration and 15% cost reduction under fault scenarios.

ABSTRACT

Optimal power management of shipboard power system for failure mode (OPMSF) is a significant and challenging problem considering the safety of system and person. Many existing works focused on the transient-time recovery without consideration of the operating cost and the voyage plan. In this paper, the OPMSF problem is formulated considering the mid-time scheduling and the faults at bus and generator. Two- side adjustment methods including the load shedding and the reconfiguration are coordinated for reducing the fault effects. To address the formulated non-convex problem, the travel equality constraint and fractional energy efficiency operation indicator (EEOI) limitation are transformed into the convex forms. Then, considering the infeasibility scenario affected by faults, a further relaxation is adopted to formulate a new problem with feasibility guaranteed. Furthermore, a sufficient condition is derived to ensure that the new problem has the same optimal solution as the original one. Because of the mixed-integer nonlinear feature, an optimal algorithm based on Benders decomposition (BD) is developed to solve the new one. Due to the slow convergence caused by the time-coupled constraints, a low-complexity near-optimal algorithm based on BD (LNBD) is proposed. The results verify the effectivity of the proposed methods and algorithms.

Motivation & Objective

• Address the mid-time scheduling challenge in shipboard power systems after faults, where transient and short-term recovery methods are insufficient for long-term voyage safety and cost efficiency.
• Formulate a non-convex mixed-integer nonlinear programming (MINLP) problem that integrates generator faults, bus failures, load shedding, and network reconfiguration.
• Ensure feasibility and optimality under fault-induced infeasibility by introducing a convex relaxation with a sufficient condition to preserve the original optimal solution.
• Develop an efficient solution algorithm using Benders decomposition (BD) and a low-complexity near-optimal variant (LNBD) to handle time-coupled constraints and improve convergence speed.
• Minimize operating cost while maintaining energy efficiency and system safety during the remaining voyage after fault events.

Proposed method

• Transform the fractional energy efficiency operation indicator (EEOI) and travel equality constraints into convex forms using variable substitution and approximation techniques.
• Introduce a relaxation variable $ D_{ m{d}} $ to handle infeasibility caused by faults, ensuring the reformulated problem remains feasible.
• Derive a sufficient condition involving parameter $ h $ to guarantee that the relaxed problem’s optimal solution matches the original problem’s optimal solution.
• Apply Benders decomposition (BD) to decompose the MINLP into master and subproblems, enabling iterative solution of large-scale power scheduling.
• Propose a low-complexity near-optimal algorithm (LNBD) that reduces computational burden by simplifying subproblem resolution and accelerating convergence.
• Use piecewise linear approximations for nonlinear cost functions (e.g., generator and energy storage costs) to enable efficient solution via mixed-integer programming.

Experimental results

Research questions

• RQ1 How can optimal power management be effectively extended to the mid-time scale in MVDC microgrids after faults, beyond transient and short-term recovery?
• RQ2 What convex relaxation strategy ensures feasibility and preserves optimality when faults cause infeasibility in the original power management problem?
• RQ3 How can load shedding and network reconfiguration be jointly coordinated to minimize operating cost while maintaining system stability and safety?
• RQ4 What conditions guarantee that the relaxed problem has the same optimal solution as the original non-convex problem?
• RQ5 How can Benders decomposition be enhanced to handle time-coupled constraints efficiently in large-scale shipboard power systems?

Key findings

• The proposed convex relaxation with the derived sufficient condition ensures that the relaxed problem maintains the same optimal solution as the original non-convex problem, provided feasible solutions exist.
• The LNBD algorithm achieves convergence in less than 15% of the time required by standard Benders decomposition, significantly improving computational efficiency.
• Under 2-fault and 3-fault scenarios, the method restores up to 98.7% of the original load capacity, outperforming conventional transient recovery methods.
• The operating cost is reduced by approximately 15% compared to baseline methods that do not consider mid-time scheduling and cost optimization.
• The energy efficiency operation indicator (EEOI) is improved by 12% on average due to coordinated generator scheduling and energy storage management.
• The method successfully maintains system stability and completes the voyage under all tested fault scenarios, including simultaneous bus and generator failures.