In the smart grid, malicious consumers can hack their smart meters to report false power consumption readings to steal electricity. Developing a machine-learning based detector for identifying these readings is a challenge due to the unavailability of malicious datasets. Most of the existing works in the literature assume attacks to compute malicious data. These detectors are trained to identify these attacks, but they cannot identify new attacks, which creates a vulnerability. Very few papers in the literature tried to address this problem by investigating anomaly detectors trained solely on benign data, but they suffer from these limitations: (1) low detection accuracy and high false alarm; (2) the need for knowledge on the malicious data to compute good detection thresholds; and (3) they cannot capture the temporal correlations of the readings and do not address the class overlapping issue caused by some deceptive attacks. To address these limitations, this paper presents a deep support vector data description (DSVDD) based unsupervised detector for false data in smart grid. Time-series readings are transformed into images, and the detector is exclusively trained on benign images. Our experimental results demonstrate the superior performance of our detectors compared to existing approaches in the literature. Specifically, our proposed DSVDD-based schemes have exhibited improvements of 0.5% to 3% in terms of recall and 3% to 9% in terms of the Area Under the Curve (AUC) when compared to existing state-of-the-art detectors.