The paper proposes a novel dual-winding active magnetic energy harvester (D-AMEH), clamped around single power line conductor carrying AC currents with time-varying magnitude while supplying a constant power DC load via an uncontrolled rectifier (e.g., 24/7 aerial marker ball lighting). To allow continuous power flow to the load despite intermittent nature of power line current magnitude, an energy storage unit (rechargeable battery) is integrated into the system via an additional secondary winding, creating an AC-coupled, isolated hybrid energy system with completely decoupled battery and load voltages. The D-AMEH simultaneously harvests the maximum power from the current-carrying conductor and feeds the load with constant power, letting the battery to seamlessly match the difference between harvested and consumed power. Analytical expressions for system currents and voltages are developed, followed by conversion losses estimation. The revealed findings are accurately supported by experiments, demonstrating close matching with corresponding analytical predictions.