  We consider a distributed optimal power flow formulated as an optimization
problem that maximizes a nondifferentiable concave function. Solving such a
problem by the existing distributed algorithms can lead to data privacy issues
because the solution information exchanged within the algorithms can be
utilized by an adversary to infer the data. To preserve data privacy, in this
paper we propose a differentially private projected subgradient (DP-PS)
algorithm that includes a solution encryption step. We show that a sequence
generated by DP-PS converges in expectation, in probability, and with
probability 1. Moreover, we show that the rate of convergence in expectation is
affected by a target privacy level of DP-PS chosen by the user. We conduct
numerical experiments that demonstrate the convergence and data privacy
preservation of DP-PS.
