Monitoring infrastructure offers functional optimisation, lower maintenance cost, security, stability and data analysis benefits. Sensor nodes require some level of energy autonomy for reliable and cost-effective operation, and energy harvesting methods have been developed in the last two decades for this purpose. Here, a power supply that collects, stores and delivers regulated power from the stray magnetic field of currentcarrying structures is presented. In cm-scale structures the skin effect concentrates current at edges at frequencies even below 1 kHz. A coil-core inductive transducer is designed. A fluxfunnelling soft magnetic core shape is used, multiplying power density by the square of funnelling ratio. A power management circuit combining reactance cancellation, voltage doubling, rectification, super-capacitor storage and switched inductor voltage boosting and regulation is introduced. The power supply is characterised in house and on a full-size industrial setup, demonstrating a power reception density of 0.36 mW/cm3, 0.54 mW/cm3 and 0.73 mW/cm3 from a 25 A RMS structural current at 360 Hz, 500 Hz and 800 Hz respectively, corresponding to the frequency range of aircraft currents. The regulated output is tested under various loads and cold starting is demonstrated. The introduced method may enable power autonomy to wireless sensors deployed in current-carrying infrastructure.