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Time series data complexity presents new challenges in clustering analysis across fields such as electricity, energy, industry, and finance. Despite advances in representation learning and clustering with Variational Autoencoders (VAE) based deep learning techniques, issues like the absence of discriminative power in feature representation, the disconnect between instance reconstruction and clustering objectives, and scalability challenges with large datasets persist. This paper introduces a novel deep time series clustering approach integrating VAE with metric learning. It leverages a VAE based on Gated Recurrent Units for temporal feature extraction, incorporates metric learning for joint optimization of latent space representation, and employs the sum of log likelihoods as the clustering merging criterion, markedly improving clustering accuracy and interpretability. Experimental findings demonstrate a 27.16% improvement in average clustering accuracy and a 47.15% increase in speed on industrial load data. This study offers novel insights and tools for the thorough analysis and application of time series data, with further exploration of VAE's potential in time series clustering anticipated in future research. [ABSTRACT FROM AUTHOR]