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Distributed Multiple Fault Detection and Estimation in DC Microgrids with Unknown Power Loads

Jingwei Dong, Mahdieh S. Sadabadi, Per Mattsson, André Teixeira

Abstract

This paper proposes a distributed diagnosis scheme to detect and estimate actuator and power line faults in DC microgrids (e.g., electric-vehicle charging microgrids) subject to unknown power loads and stochastic noise. To address actuator faults, we develop an optimization-based filter design approach within the differential-algebraic equation (DAE) framework, which achieves fault estimation, decoupling from power line faults, and robustness against noise. In contrast, the estimation of power line faults poses greater challenges due to the inherent coupling between fault currents and unknown power loads, especially under insufficient system excitation, where their effects become difficult to distinguish from measurements. To the best of our knowledge, this is the first study to address this critical yet underexplored issue. Our solution introduces a novel differentiate-before-estimate strategy. A set of diagnosis rules based on the temporal characteristics (i.e., duration of threshold violation) of a constructed residual is developed to distinguish step load changes from line faults. Once a power line fault is detected, a regularized least-squares (LS) method is activated to estimate the fault currents, for which we further derive an upper bound on the estimation error. Finally, comprehensive simulations validate the effectiveness of the proposed scheme in terms of estimation accuracy and robustness against disturbances and noise under different fault scenarios.

Distributed Multiple Fault Detection and Estimation in DC Microgrids with Unknown Power Loads

Abstract

This paper proposes a distributed diagnosis scheme to detect and estimate actuator and power line faults in DC microgrids (e.g., electric-vehicle charging microgrids) subject to unknown power loads and stochastic noise. To address actuator faults, we develop an optimization-based filter design approach within the differential-algebraic equation (DAE) framework, which achieves fault estimation, decoupling from power line faults, and robustness against noise. In contrast, the estimation of power line faults poses greater challenges due to the inherent coupling between fault currents and unknown power loads, especially under insufficient system excitation, where their effects become difficult to distinguish from measurements. To the best of our knowledge, this is the first study to address this critical yet underexplored issue. Our solution introduces a novel differentiate-before-estimate strategy. A set of diagnosis rules based on the temporal characteristics (i.e., duration of threshold violation) of a constructed residual is developed to distinguish step load changes from line faults. Once a power line fault is detected, a regularized least-squares (LS) method is activated to estimate the fault currents, for which we further derive an upper bound on the estimation error. Finally, comprehensive simulations validate the effectiveness of the proposed scheme in terms of estimation accuracy and robustness against disturbances and noise under different fault scenarios.

Paper Structure

This paper contains 22 sections, 5 theorems, 82 equations, 18 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Main Contributions
  4. Model Description and Problem Statement
  5. DG Dynamics
  6. Power Line Dynamics
  7. Stabilizing Voltage Controller
  8. Closed-loop Dynamics
  9. Problem Statement.
  10. Estimation of Actuator Faults
  11. Estimation of aggregate faulty line current
  12. Design of Pre-filter $1$
  13. Design of Line Current Estimators
  14. Design of Pre-filter $2$
  15. Design of Faulty Line Current Estimator
  16. ...and 7 more sections

Key Result

Proposition 3.1

Consider the closed-loop dynamics of DG unit $i$ (for $i \in \mathbb{N}_G$) in eq: Faulty DG subject to the actuator fault $f_{a,i}$. The design conditions eq: decouple con-eq: estimation con for the estimation filter structured in eq: filter can be equivalently formulated into the following linear where $\bar{H_i}$ is given by

Figures (18)

  • Figure 1: Structure of a DC microgrid.
  • Figure 2: Structure of DG $i$ with the diagnosis component: block $\mathcal{D}_{a,i}$ for the actuator fault $f_{a,i}$ and block $\mathcal{D}_{l,i}$ for the aggregate faulty line current $f_{I,i}$, where $\mathbb{N}_i$ denote the set of neighboring units of DG $i$.
  • Figure 3: Structure of the diagnosis block $\mathcal{D}_{l,i}$.
  • Figure 4: Dynamic response of the DC microgrid when considering the actuator fault.
  • Figure 5: Diagnosis of the actuator fault: (a) results of $\mathcal{D}_{a,1}$, (b) results of $\mathcal{D}_{a,2}$, and (c) results of $\mathcal{D}_{a,3}$.
  • ...and 13 more figures

Theorems & Definitions (18)

  • Remark 2.2: Applicability beyond additive faults
  • Proposition 3.1: Actuator fault estimation
  • proof
  • Remark 3.2: Differences with previous work
  • Proposition 4.1: Discrimination between step load changes and power line faults
  • proof
  • Remark 4.2: Selection of $T$
  • Proposition 4.3: Analytical solution
  • proof
  • Theorem 4.4: Performance bound of the regularized estimator
  • ...and 8 more