Verified Bounds on the Charging Gain From Reactive Power at Battery-Buffered Electric Vehicle Fast-Charging Stations

Abstract A battery that supports a fast-charging station has to be recharged through the same feeder, and its converter can supply reactive power while it charges. This paper quantifies how much additional charging that reactive capability admits and how firmly the estimate can be stated. For each control policy, an AC-feasible operating point is paired with an upper bound from an outer linear approximation of the branch-flow relaxation; the dual bound is evaluated in rational arithmetic. A fixed command is then checked over a continuous box of load and source-voltage uncertainty with an invariant voltage enclosure. Four balanced feeders (16, 33, 69, and 141 buses) and controlled changes of R/X ratio, upstream short-circuit level, connectivity, and head-branch rating separate voltage, thermal, and converter limits. At the representative 33-bus location, reactive dispatch raises admissible charging from 250.57 kW to 469.35 kW, and the optimization bracket that remains is 1.1×10 − 4 kW. A Volt-VAR curve tuned for the same state inside the IEEE 1547 Category B setting ranges reaches the same value, so the 124.52-kW shortfall of the default curve is a setting effect. A tuned curve frozen across load levels loses 5.60 kW at the held-out state. In a public 33-bus case, reactive support relieves a binding head-branch limit while the local voltage stays inside the default dead band. All 3340 reported operating points were re-solved with MATPOWER and OpenDSS: voltage magnitudes agree within 7.6×10 –10 p.u., and no admitted point violates a network limit.