In the last decade, researchers have been investigating the severity of insulation breakdown caused by partial discharge (PD) in overhead transmission lines with covered conductors or electrical equipment such as generators and motors used in various industries. Developing an effective partial discharge detection system can lead to significant savings on maintenance and prevent power disruptions. Traditional methods rely on hand-crafted features and domain expertise to identify partial discharge patterns in the electrical current. Many data-driven deep learning-based methods have been proposed in recent years to remove these ad hoc feature extraction. However, most of these methods either operate in the time-domain or frequency-domain. Many research approaches have been developed to generate phase-resolved partial discharge (PRPD) patterns from raw PD sensor data. These PRPD diagrams suggest a correlation between partial discharge activities occurring in an alternating electrical waveform's positive and negative half-cycles. However, this correlation criterion between half-cycles has been remained unexplored in deep learning-based methods. This work proposes a novel feature-fusion-based Dual-CyCon Net that can utilize all time, frequency, and phase domain features for joint learning in one cohesive framework. Our proposed cycle-consistency loss exploits any relation between an alternating electrical signal's positive and negative half-cycles to calibrate the model's sensitivity. This loss explores cycle-invariant PD-specific features, enabling the model to learn more robust, noise-invariant features for PD detection. A case study of our proposed framework on a public real-world noisy measurement from high-frequency voltage sensors to detect damaged power lines has achieved a state-of-the-art MCC score of 0.8455.