Privacy of Distributed Optimality Schemes in Power Networks

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.