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

Abstract: 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.