Data quality issues exist in practical phasor measurement units (PMUs) due to communication errors or signal interferences. As a result, the performances of existing data-driven disturbance classification methods can be significantly affected. In this article, a fast disturbance classification method that is robust to PMU data quality issues is proposed. The impacts of bad PMU measurements on disturbance classification are investigated by analyzing the feature distributions of deep learning methods. A new feature extraction scheme that uses the univariate temporal convolutional denoising autoencoder (UTCN-DAE) is proposed. It allows encoding and decoding univariate disturbance data through a temporal convolutional network to capture the temporal feature representation and is robust to bad data. Based on the features of the frequency and voltage measurements encoded by the UTCN-DAE, a two-stream enhanced network, i.e., the multivariable temporal convolutional denoising network is proposed to achieve optimal feature extraction of multivariate time series by feature fusion. The classification is performed using a multilayered deep neural network and Softmax classifier. Extensive results obtained on the IEEE 39-bus system as well as a large-scale power system in China with field PMU measurements show that the proposed method achieves the highest classification accuracy and computational efficiency as compared to other deep learning algorithms.