Search

Abstract The differential privacy (DP) literature often centers on meeting privacy constraints by introducing noise to the query, typically using a pre-specified parametric distribution model with one or two degrees of freedom. However, this emphasis tends to neglect the crucial considerations of response accuracy and utility, especially in the context of categorical or discrete numerical database queries, where the parameters defining the noise distribution are finite and could be chosen optimally. This paper addresses this gap by introducing a novel framework for designing an optimal noise probability mass function (PMF) tailored to discrete and finite query sets. Our approach considers the modulo summation of random noise as the DP mechanism, aiming to present a tractable solution that not only satisfies privacy constraints but also minimizes query distortion. Unlike existing approaches focused solely on meeting privacy constraints, our framework seeks to optimize the noise distribution under an arbitrary $$(\epsilon , \delta )$$ ( ϵ , δ ) constraint, thereby enhancing the accuracy and utility of the response. We demonstrate that the optimal PMF can be obtained through solving a mixed-integer linear program. Additionally, closed-form solutions for the optimal PMF are provided, minimizing the probability of error for two specific cases. Numerical experiments highlight the superior performance of our proposed optimal mechanisms compared to state-of-the-art methods. This paper contributes to the DP literature by presenting a clear and systematic approach to designing noise mechanisms that not only satisfy privacy requirements but also optimize query distortion. The framework introduced here opens avenues for improved privacy-preserving database queries, offering significant enhancements in response accuracy and utility.

Abstract Fast‐acting smart inverters that utilize preset operating conditions to determine real and reactive power injection/consumption can create voltage instabilities (over‐voltage, voltage oscillations and more) in an electrical distribution network if set‐points are not properly configured. In this work, linear distribution power flow equations and droop‐based Volt–Var and Volt–Watt control curves are used to analytically derive a stability criterion using Lyapunov analysis that includes the network operating condition. The methodology is generally applicable for control curves that can be represented as Lipschitz functions. The derived Lipschitz constants account for smart inverter hardware limitations for reactive power generation. A local policy is derived from the stability criterion that allows inverters to adapt their control curves by monitoring only local voltage, thus avoiding centralized control or information sharing with other inverters. The criterion is independent of the internal time‐delays of smart inverters. Simulation results for inverters with and without the proposed stabilization technique demonstrate how smart inverters can mitigate voltage oscillations locally and mitigate real and reactive power flow disturbances at the substation under multiple scenarios. The study concludes with illustrations of how the control policy can dampen oscillations caused by solar intermittency and cyberattacks.