Strategic risk aversion of smart energy hubs in the joined energy markets applying a stochastic game approach

Multi-carrier energy systems are defined as a concept within the energy hub notion. The energy hub operator aims to investigate maximizing the system profit through strategic behaviors and optimal bidding when participating in joined energy markets containing natural gas and electric power. Bi-level programming is applied for such conditions dividing the complex problem into two separate levels. In the upper-level structure, each energy hub seeks profit maximization. In the lower level structure, market clearing is found to maximize the social welfare of the system. Game-theoretic approaches as mathematical programming with equilibrium constraints (MPEC) solve the bi-level programming. In this regard, the Monte-Carlo simulation is applied to incorporate renewable energy uncertainty and intermittency nature. The MPECs form an equilibrium programming with equilibrium constraints (EPEC) to solve the defined approach. Furthermore, the Conditional Value at Risk (CVaR) algorithm is applied to the risk aversion decision-making. Hence, applying the CVaR in a game setting of multi-energy carriers using bi-level programming in a renewable-based environment is the main contribution of the current paper. Two case studies are defined to determine the efficacy and correctness of the introduced structure. One example, containing one energy hub as the primary unit and another as a rival unit, is investigated to verify the joined energy market model. Another standard case study is conducted to confirm the proposed model's flexibility in congested and uncongested networks. The study's main implications are three-folded: the proposed model can provide the uniqueness and existence of the Nash equilibria. The values of strategic biddings in the congested mode are higher than those in the uncongested mode when both players act strategically. The CVaR results prove that risk aversion causes the system to be more vulnerable economically.