Anomaly detection is an important task in power systems. To make better use of the phasor measurement unit (PMU) data collected from a low observability power system for anomaly detection, a data dimensionality increment algorithm is proposed in this paper. First, a low-dimensional spatio-temporal data matrix is formulated by using the synchrophasor measurements collected from a limited number of PMUs in a power system. Then, a data dimensionality increment algorithm based on random tensor theory (RTT) is proposed for anomaly detection. The proposed algorithm can help improve the sensitivity of random matrix theory (RMT) based and machine learning (ML) based anomaly detection approaches, and it is able to accelerate the convergence rate of model training in the ML based anomaly detection approach. Case studies on the IEEE 118-bus test system validate the effectiveness of the proposed algorithm.