Differential-privacy preserving optimal power flow in smart grid

In smart grid, the smart meters improve the grids' efficiency but imply the sensitive residential information. Hence, how to prevent privacy leakage of smart meter data has drawn lots of researchers' attentions. Yet, it is non-trivial to quantify the relation between privacy protection behaviours and system utility loss. To this end, the authors leverage the notion of differential privacy (DP) to measure the privacy-protection strength, under the framework of optimal power flow (OPF). Specifically, once the noise is injected to hide the actual demand, the solutions of OPF problem are probably affected, which undermine the grid utility. In this study, the authors are the first quantitatively investigating DP preserving OPF problem. Starting with re-modelling the noise-injected OPF problem, the authors rigorously prove OPF solution's sensitivity with respect to the uncertainty of demand. Moreover, aiming at OPF-based pricing mechanism, locational marginal pricing (LMP), the respective privacy-protection's contribution on LMPs is explicitly expressed. Subsequently, based on the extensive experiments, it is illustrated that the quantitative correlation between the privacy-protection strength and the gird system performance. Furthermore, by combining the grid topology and privacy-protection strength, a novel billing system to fairly charge the extra payment to subsidise the privacy-insensitive customers is proposed.