This paper proposes a high efficient approach for power disturbance waveform (PDW) compression in the view of Heisenberg uncertainty. The key idea is trying to represent each signal component of PDW by nonzero coeffients as few as possible with the uncertainty principle restriction. PDWs are projected in a union of bases (UB), and each signal component of the PDWs can be represented very sparsely. The UB decomposition is solved by orthogonal matching pursuit (OMP). The features and cross correlation of subbases of the UB guarantee the PDW compression with high compression ratio and recovered accuracy. With various simulated and field PDWs tests, the compressed data size of the new method is proved with good characteristics such as low sensitivity to sampling frequency increment and to types of signal components contained in PDWs. Besides, it is found that the new method and methods which employ wavelet techniques share similar effect of noise for PDW compression. The proposed method is also applied in a 220kV power substation for field PDWs compression from fault recorders. The comparisons, analyses and experiments indicate that the proposed method has a high PDWs compression efficiency for future power grid monitoring.