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Timely and accurate detection of events affecting the stability and reliability of power transmission systems is crucial for safe grid operation. This paper presents an efficient unsupervised machine-learning algorithm for event detection using a combination of discrete wavelet transform (DWT) and convolutional autoencoders (CAE) with synchrophasor phasor measurements. These measurements are collected from a hardware-in-the-loop testbed setup equipped with a digital real-time simulator. Using DWT, the detail coefficients of measurements are obtained. Next, the decomposed data is then fed into the CAE that captures the underlying structure of the transformed data. Anomalies are identified when significant errors are detected between input samples and their reconstructed outputs. We demonstrate our approach on the IEEE-14 bus system considering different events such as generator faults, line-to-line faults, line-to-ground faults, load shedding, and line outages simulated on a real-time digital simulator (RTDS). The proposed implementation achieves a classification accuracy of 97.7%, precision of 98.0%, recall of 99.5%, F1 Score of 98.7%, and proves to be efficient in both time and space requirements compared to baseline approaches.