PQDs have adverse impacts on the safe operation and reliability of the modern integrated power system so it is of great necessity to identify them. Existence of missing measurement data hinders accurate identification of potential PQDs and the inevitable discrepancy after data recovery vitiates the current detection methods. Besides, the related research is lacked. In this article, a novel unified framework of Wasserstein adversarial learning is proposed on identifying PQDs with incomplete data for the first time. It consists of WAI and WADA. WAI minimizes the improved Wasserstein distance between the data distributions of observed and generated PQD parts to impute missing values. During this process, PQD characteristics can be well recovered. Then, WADA leverages the Wasserstein domain discrepancy between the feature distributions of source labeled complete and target unlabeled imputed PQDs to capture domain-invariant features. Thus, labels of target imputed PQDs can be predicted accurately. Experimental verification demonstrates that the proposed WAI and WADA outperform other typical methods with better imputation results and higher classification accuracy. Constrained Wasserstein loss empowers the proposed deep learning models with excellent convergence and gradient stability.