Although distribution grid customers are obliged to share their consumption
data with distribution system operators (DSOs), a possible leakage of this data
is often disregarded in operational routines of DSOs. This paper introduces a
privacy-preserving optimal power flow (OPF) mechanism for distribution grids
that secures customer privacy from unauthorised access to OPF solutions, e.g.,
current and voltage measurements. The mechanism is based on the framework of
differential privacy that allows to control the participation risks of
individuals in a dataset by applying a carefully calibrated noise to the output
of a computation. Unlike existing private mechanisms, this mechanism does not
apply the noise to the optimization parameters or its result. Instead, it
optimizes OPF variables as affine functions of the random noise, which weakens
the correlation between the grid loads and OPF variables. To ensure feasibility
of the randomized OPF solution, the mechanism makes use of chance constraints
enforced on the grid limits. The mechanism is further extended to control the
optimality loss induced by the random noise, as well as the variance of OPF
variables. The paper shows that the differentially private OPF solution does
not leak customer loads up to specified parameters
