arXiv:2610.41212v1 Announce Type: new Abstract: Low-voltage ride-through (LVRT) forces a grid-following inverter to allocate finite converter current between active- and reactive-current objectives. This paper uses a PSCAD electromagnetic-transient (EMT) representation of an aggregated battery energy storage system (BESS) to quantify how short-circuit ratio (SCR) and grid impedance X/R ratio alter that tradeoff. Active-current priority and reactive-current priority are compared for five paired grid conditions under the same 150-ms balanced three-phase fault, with pre-fault active power approximately 0.84 pu, POI reactive-power exchange near 0 pu, and a 1.0-pu dq-current limit. Fundamental positive-sequence voltage and power are reconstructed from 100-$\mu$s three-phase EMT outputs. Across the fixed-fault SCR sweep, the Q-priority late-fault voltage advantage increases from 0.046 pu in the strongest tested grid to 0.129 pu in the weakest; the weakest P-priority case also shows active-power reversal and a pronounced controller-frequency excursion. At fixed SCR, changing X/R produces a smaller increase from 0.092 to 0.112 pu, mainly through reduced P-priority voltage support. Because the common physical fault also deepens the passive retained-voltage condition as SCR decreases, the SCR result is interpreted as a fixed-fault grid-strength sensitivity rather than a constant-sag comparison. Grid strength is the larger sensitivity in the tested matrix, while X/R remains an additional modifier under the studied fault conditions.