Smart meter devices enable a better understanding of the demand at the potential risk of private information leakage. One promising solution to mitigating such risk is to inject noises into the meter data to achieve a certain level of differential privacy. In this paper, we cast one-shot non-intrusive load monitoring (NILM) in the compressive sensing framework, and bridge the gap between theoretical accuracy of NILM inference and differential privacy's parameters. We then derive the valid theoretical bounds to offer insights on how the differential privacy parameters affect the NILM performance. Moreover, we generalize our conclusions by proposing the hierarchical framework to solve the multi-shot NILM problem. Numerical experiments verify our analytical results and offer better physical insights of differential privacy in various practical scenarios. This also demonstrates the significance of our work for the general privacy preserving mechanism design.
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