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Time-Domain Operational Metrics for Real-time Resilience Assessment in DC Microgrids

Maral Shadaei, Ali Hosseinipour, Javad Khazaei

TL;DR

The paper addresses the need for real-time resilience assessment in medium-voltage DC (MVDC) shipboard microgrids by introducing time-domain, voltage-based metrics. It develops a reduced-order MVDC model and a degradation framework, and defines three metrics: $R_V(t)=\int (v_{o_{DC}}-v_t(t)) dt$, $V_{DI}=k\frac{\int_{t_d}^{t_r}(v_{o_{DC}}-v_t(t))dt}{v_{o_{DC}}(t_r-t_d)}$, and $V_{REI}=\frac{\int_{t_r}^{t_{pr}}(v_t(t)-V_{pe}) dt}{(v_{o_{DC}}-V_{pe})(t_{pr}-t_r)}$, combined as $\Re = \xi(R_V,V_{DI},V_{REI})$ to enable real-time monitoring of degradation, recovery, and overall resilience. The framework is validated through MATLAB/Simulink simulations of events such as sudden load changes and generator outages, demonstrating that $V_{REI}$ correlates with inertia via $C_{eq}$ and that the metrics provide actionable, online insights for operators. The contributions offer a practical, real-time tool for enhancing the resilience of Navy MVDC microgrids by capturing multiple event phases directly from DC bus voltage dynamics.

Abstract

Resilience is emerging as an evolving notion, reflecting a system's ability to endure and adapt to sudden and catastrophic changes and disruptions. This paper spotlights the significance of the quantitative resilience indices of medium-voltage DC (MVDC) distribution technology in marine vessels, notably naval ships. Given the intricate electrical requirements of modern naval ships, the need for a robust power supply underlines the imperative of resilient DC microgrids. Addressing this, our study introduces a novel quantitative metric for operational resilience of DC microgrids based on the measured voltage of main DC bus. This metric not only fuses real-time tracking, compatibility, and computational efficiency, but also adeptly monitors multiple event phases based on time-domain analysis of dc bus voltage dynamics. The intricacies of the dc bus voltage, including overshoots and undershoots, are meticulously accounted for in the algorithm design. With respect to existing research that typically focuses on offline resilience assessments, the proposed index provides valuable real-time information for microgrid operators and identifies whether microgrid resilience is deteriorating over time.

Time-Domain Operational Metrics for Real-time Resilience Assessment in DC Microgrids

TL;DR

The paper addresses the need for real-time resilience assessment in medium-voltage DC (MVDC) shipboard microgrids by introducing time-domain, voltage-based metrics. It develops a reduced-order MVDC model and a degradation framework, and defines three metrics: , , and , combined as to enable real-time monitoring of degradation, recovery, and overall resilience. The framework is validated through MATLAB/Simulink simulations of events such as sudden load changes and generator outages, demonstrating that correlates with inertia via and that the metrics provide actionable, online insights for operators. The contributions offer a practical, real-time tool for enhancing the resilience of Navy MVDC microgrids by capturing multiple event phases directly from DC bus voltage dynamics.

Abstract

Resilience is emerging as an evolving notion, reflecting a system's ability to endure and adapt to sudden and catastrophic changes and disruptions. This paper spotlights the significance of the quantitative resilience indices of medium-voltage DC (MVDC) distribution technology in marine vessels, notably naval ships. Given the intricate electrical requirements of modern naval ships, the need for a robust power supply underlines the imperative of resilient DC microgrids. Addressing this, our study introduces a novel quantitative metric for operational resilience of DC microgrids based on the measured voltage of main DC bus. This metric not only fuses real-time tracking, compatibility, and computational efficiency, but also adeptly monitors multiple event phases based on time-domain analysis of dc bus voltage dynamics. The intricacies of the dc bus voltage, including overshoots and undershoots, are meticulously accounted for in the algorithm design. With respect to existing research that typically focuses on offline resilience assessments, the proposed index provides valuable real-time information for microgrid operators and identifies whether microgrid resilience is deteriorating over time.
Paper Structure (9 sections, 1 theorem, 8 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 9 sections, 1 theorem, 8 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Model Description
  4. Reduced order model of MVDC shipboard microgrids
  5. MG degredation model
  6. Proposed Time-domain Voltage Resiliency Index
  7. Simulation results
  8. Case studies
  9. Conclusion

Key Result

Theorem 3.1

The trapezoidal rule estimates the integral of a function by approximating the area under its graph as trapezoids. For enhanced accuracy, one can partition the interval into smaller subintervals. Let $\left\{x_k\right\}$ be a partition of $[a, b]$ such that $a=x_0<\cdots<x_{N-1}<x_N=b$ and $\Delta x For uniform subintervals of size $\Delta x$, the formula simplifies to trap:

Figures (6)

  • Figure 1: Closed-loop MVDC microgrid configuration for Navy shipboards.
  • Figure 2: Verifying the calculation-based model under sudden load change.
  • Figure 3: Microgrid voltage performance curve during an event.
  • Figure 4: DC bus voltage and the $R_V$ index verification.
  • Figure 5: Voltage degradation index verification.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Theorem 3.1
  • Remark
  • Remark