Edge computing is becoming a mainstream platform for practical applications of machine learning and in particular deep learning. Many systems capable of efficient execution of deep neural models in the context of edge computing are readily available or beginning to appear on the consumer market. The Jetson platform from NVIDIA, the Neural stick from Intel, and the Edge TPU designed by Google are examples of devices that enable the application of complex neural networks in edge computing. This work investigates the ability of selected edge devices to address a real-world classification problem from electrical power engineering. It consists of the detection of partial discharges (PDs) from covered conductors (CCs) on high-voltage power lines. The CCs are used in heavily forested and generally inaccessible areas where clearance zones cannot be maintained. Detection of PDs can prevent forest fires and other disasters potentially caused by prolonged contact of CCs with vegetation. The problem is suitable for an edge computing-based solution because Internet connectivity in remote areas is usually insufficient and a 2G (GSM) mobile network is available at best. Because such locations are difficult to access and usually without a suitable power supply, the proposed solution puts an emphasis also on PD detection latency and the associated power consumption. Two principal approaches to PD detection are considered. One is based on the classification of 1D time series (raw data). The second approach uses the signal transformed into a 2D spectrogram. In this case, two types of algorithms are evaluated. The first one is a novel custom stacking ensemble detector composed of 2D convolutional neural networks and a neural meta-learner on top of it. The second one uses the well-known and widely-used used ResNet deep neural model.