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Current monitoring of multi-core cables plays an important role in various applications since cables are widely utilized in distribution and transmission systems. However, existing current sensing devices which are mostly designed for the single conductor break the cable jacket to measure conductor currents in multi-core cables. Recently various non-invasive sensing devices with reconstruction algorithms are designed for rapid access to currents in multi-core cables but don't make full use of abundant information during current monitoring. Thus, this paper proposes an event-driven non-invasive multi-core cable current monitoring method using an array of magnetic field sensors. Real-time currents of the multi-core cable are determined by solving conductor localization and current measurement problems. Since the observed changes of the magnetic field around the cable are caused by current or position changes, conductor localization is driven by the events which are classified as electrical events and mechanical events respectively. The key idea is to improve the accuracy of conductor localization through effective electrical events. Then current monitoring is achieved by solving current measurement problems using more accurate conductor positions and the measured magnetic field. This method is utilized in the real cable current monitoring, a sustaining decrease of relative current errors is observed, which is below 1% in long-term monitoring.