  This paper introduces a differentially private mechanism to protect the
information exchanged during the coordination of the sequential market-clearing
of electricity and natural gas systems. The coordination between these
sequential and interdependent markets represents a classic Stackelberg game and
relies on the exchange of sensitive information between the system agents,
including the supply and demand bids in each market or the characteristics of
the systems. The paper is motivated by the observation that traditional
differential privacy mechanisms are unsuitable for the problem of interest: The
perturbation introduced by these mechanisms fundamentally changes the
underlying optimization problem and even leads to unsatisfiable instances. To
remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg
Mechanism (PPSM), a framework that enforces the notions of consistency and
fidelity of the privacy-preserving information to the original problem
objective. The PPSM has strong properties: It complies with the notion of
differential privacy and ensures that the outcomes of the privacy-preserving
coordination mechanisms are close-to-optimality for each agent. The fidelity
property is analyzed by providing theoretical guarantees on the cost of privacy
of PPSM and experimental results on several gas and electricity market
benchmarks based on a real case study demonstrate the effectiveness of the
approach.
