Harmonic Ratio Analysis (HRA) for Load-Dependent Detection of H₂ Crossover in Membrane Electrolyzers: Stack, Cell-Group and Single-Cell Diagnostics across DC Load Points for PEM and AEM Systems

This technical note describes a load-dependent Harmonic Ratio Analysis (HRA) approach for detecting H₂ crossover-related signatures in membrane electrolyzers. It focuses on PEM and AEM systems and extends HRA from a single global nonlinear indicator to a load-resolved and spatially resolved diagnostic method.

Hydrogen crossover is relevant for safety, product-gas purity, Faradaic efficiency, hydrogen yield, and stack ageing. The note discusses why H₂-in-O₂ formation, local reactive gas mixtures, pressure imbalance, dynamic operation, high current density, membrane state, temperature and water management require diagnostic approaches that go beyond stationary single-point measurements.

The central diagnostic quantity is the load-dependent second-harmonic ratio R₂(I_DC) = |H₂(I_DC)| / |H₁(I_DC)|. The method evaluates this metric across defined DC load points or DC load classes instead of using a single threshold. Even-harmonic contributions are interpreted as indicators of asymmetric nonlinear processes. A crossover-related interpretation requires load dependence, persistence logic, reference bands, artefact exclusion and plausibility checks using pressure, temperature or gas data.

A key focus of the note is multi-channel HRA over the stack. While stack-level HRA provides a useful summation signal, local defects can be diluted or masked. Cell-group and single-cell HRA maps R₂,k(I_DC) provide higher spatial resolution and can help identify local membrane defects, seal issues, uneven compression, water-distribution problems or gas accumulation. The method is positioned as an electrical early indicator and diagnostic trigger, not as a replacement for direct gas analysis, certified safety sensors or standards-compliant protection functions.

The technical note includes the HRA principle, DC load-dependent reference-band logic, multi-channel stack interpretation, reproducible measurement recommendations, illustrative operating examples, limitations, safety boundaries and a comparison with direct crossover evidence, EIS and THD.