Instance selection is a vital technique for energy big data analytics. It is challenging to process a massive amount of streaming data generated at high speed rates by intelligent monitoring devices. Instance selection aims at removing noisy and bad data that can compromise the performance of data-driven learners. In this context, this paper proposes a novel similarity based instance selection (SIS) method for real-time phasor measurement unit data. In addition, we develop a variant of the Hoeffding-Tree learner enhanced with the SIS for classifying disturbances and cyber-attacks. We validate the merits of the proposed learner by exploring its performance under four scenarios that affect either the system physics or the monitoring architecture. Our experiments are simulated by using the datasets of industrial control system cyber-attacks. Finally, we conduct an implementation analysis which shows the deployment feasibility and high-performance potential of the proposed learner, as a part of real-time monitoring applications.