  The increasing participation of local generation and controllable demand
units within the power network motivates the use of distributed schemes for
their control. Simultaneously, it raises two issues; achieving an optimal power
allocation among these units, and securing the privacy of the generation/demand
profiles. This study considers the problem of designing distributed optimality
schemes that preserve the privacy of the generation and controllable demand
units within the secondary frequency control timeframe. We propose a consensus
scheme that includes the generation/demand profiles within its dynamics,
keeping this information private when knowledge of its internal dynamics is not
available. However, the prosumption profiles may be inferred using knowledge of
its internal model. We resolve this by proposing a privacy-preserving scheme
which ensures that the generation/demand cannot be inferred from the
communicated signals. For both proposed schemes, we provide analytic stability,
optimality and privacy guarantees and show that the secondary frequency control
objectives are satisfied. The presented schemes are distributed, locally
verifiable and applicable to arbitrary network topologies. Our analytic results
are verified with simulations on a 140-bus system, where we demonstrate that
the proposed schemes offer enhanced privacy properties, enable an optimal power
allocation and preserve the stability of the power network.
