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In this paper, we investigate a novel real-time pricing scheme, which considers both renewable energy resources and traditional power resources and could effectively guide the participants to achieve individual welfare maximization in the system. To be specific, we develop a Lagrangian-based approach to transform the global optimization conducted by the power company into distributed optimization problems to obtain explicit energy consumption, supply, and price decisions for individual participants. Also, we show that these distributed problems derived from the global optimization by the power company are consistent with individual welfare maximization problems for end-users and traditional power plants. We also investigate and formalize the vulnerabilities of the real-time pricing scheme by considering two types of data integrity attacks: Ex-ante attacks and Ex-post attacks, which are launched by the adversary before or after the decision-making process. We systematically analyze the welfare impacts of these attacks on the real-time pricing scheme. Through a combination of theoretical analysis and performance evaluation, our data shows that the proposed real-time pricing scheme could effectively guide the participants to achieve welfare maximization, while cyber-attacks could significantly disrupt the results of real-time pricing decisions, imposing welfare reduction on the participants.

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