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This paper introduces a differentially private mechanism to protect theinformation exchanged during the coordination of the sequential market-clearingof electricity and natural gas systems. The coordination between thesesequential and interdependent markets represents a classic Stackelberg game andrelies on the exchange of sensitive information between the system agents,including the supply and demand bids in each market or the characteristics ofthe systems. The paper is motivated by the observation that traditionaldifferential privacy mechanisms are unsuitable for the problem of interest: Theperturbation introduced by these mechanisms fundamentally changes theunderlying optimization problem and even leads to unsatisfiable instances. Toremedy such limitation, the paper introduces the Privacy-Preserving StackelbergMechanism (PPSM), a framework that enforces the notions of consistency andfidelity of the privacy-preserving information to the original problemobjective. The PPSM has strong properties: It complies with the notion ofdifferential privacy and ensures that the outcomes of the privacy-preservingcoordination mechanisms are close-to-optimality for each agent. The fidelityproperty is analyzed by providing theoretical guarantees on the cost of privacyof PPSM and experimental results on several gas and electricity marketbenchmarks based on a real case study demonstrate the effectiveness of theapproach.

PPSM: A Privacy-Preserving Stackelberg Mechanism: Privacy Guarantees for the Coordination of Sequential Electricity and Gas Markets