Statistically Adaptive Differential Protection for AC Microgrids Based on Kullback-Leibler Divergence

TL;DR

This work tackles protection of AC microgrids with abundant inverter-based resources, where traditional schemes struggle due to variable fault currents and transients. It introduces a statistically adaptive differential protection framework that uses a Bartlett-corrected G-statistic on log-transformed per-phase currents and a Mahalanobis-distance detector with thresholds derived from the $\chi^2$ distribution, enabling controlled false alarms. A two-phase offline-online workflow, including Bayesian-optimized adaptive histogram binning and a hierarchical fault classifier with temporal persistence, yields sub-cycle detection and high fault-detection/classification accuracy even under high-impedance faults and noisy conditions. Simulations on a modified CIGRE 14-bus microgrid demonstrate robust performance across grid-connected and islanded modes, with tolerance to 10 ms communication delay and noise levels down to 20 dB SNR, highlighting the approach's practicality and scalability for next-generation microgrid protection.

Abstract

The proliferation of inverter-based resources challenges traditional microgrid protection by introducing variable fault currents and complex transients. This paper presents a statistically adaptive differential protection scheme based on Kullback-Leibler divergence, implemented via a Bartlett-corrected G-statistic computed on logarithm-transformed current magnitudes. The method is a multivariate fault detection engine that employs the Mahalanobis distance to distinguish healthy and faulty states, enabling robust detection even in noisy environments. Detection thresholds are statistically derived from a chi-squared distribution for precise control over the false alarm rate. Upon detection, a lightweight classifier identifies the fault type by assessing per-phase G-statistics against dedicated thresholds, enhanced by a temporal persistence filter for security. Extensive simulations on a modified CIGRE 14-bus microgrid show high efficacy: sub-cycle average detection delays, high detection and classification accuracy across operating modes, resilience to high-impedance faults up to 250 Ohms, tolerance to 10 ms communication delay, and noise levels down to a 20 dB signal-to-noise ratio. These findings demonstrate a reproducible and computationally efficient solution for next-generation AC microgrid protection.

Figures (9)

• Figure 1: Workflow overview: Offline phase—design features, calibrate the reference model, and store it for online use; Online phase—compute per-phase statistics, perform fault detection, and classify faults.
• Figure 2: Single-line diagram of the modified CIGRE 14-bus microgrid test system.
• Figure 3: Time-domain response of detection and classification for a 50 $\Omega$ LG fault on line 01–02 (grid-connected). The fault begins at $t=1.0$ s. Detection occurs at $t=1.006$ s as $D_{\!M}^2$ exceeds $\tau_{\mathrm{det}}$, then it is classified as ag by the relative jump test in the phase-a G-statistic and by the zero-sequence statistic $g_0^{*}(t)$ crossing its absolute threshold.
• Figure 4: Time-domain response of detection and classification for an LL fault on line 03–04 (islanded). The fault occurs at $t=1.0$ s. $D_{\!M}^{2}$ crosses $\tau_{\mathrm{det}}$ at $t=1.010$ s. Then $z_b(t)$ and $z_c(t)$ cross their respective thresholds, correctly identifying the event as bc.
• Figure 5: Response of $D_{\!M}^{2}$ to a sequence of challenging events on feeder 03–08. After reconfiguration and islanding, an LLL fault is initiated at $t=3.0$ s. The index crosses $\tau_{\mathrm{det}}$ and remains stable, even as a $50\%$ load increase (at $t=4.0$ s) and DER output reduction (at $t=5.0$ s) create more adverse operating conditions.