A bilevel stochastic programming problem (BSPP) model of the decision-making of an energy hub manager is presented. Hub managers seek ways to maximize their profit by selling electricity and heat. They have to make decisions about: (1) the level of involvement in forward contracts, electricity pool markets, and natural gas networks and (2) the electricity and heat offering prices to the clients. These decisions are made under uncertainty of pool prices, demands as well as the prices offered by rival hub managers. On the other hand, the clients try to minimize the total cost of energy procurement. This two-agent relationship is presented as a BSPP in which the hub manager is placed in the upper level and the clients in the lower one. The bilevel scheme is converted to its equivalent single-level scheme using the Karush-Kuhn-Tucker optimality conditions although there are two bilinear products related to electricity and heat. The heat bilinear product is replaced by a heat price-quota curve and the electricity bilinear product is linearized using the strong duality theorem. In addition, conditional value at risk is used to reduce the unfavorable effects of the uncertainties. The effectiveness of the proposed model is evaluated in various simulations of a realistic case study.

Co-designing energy systems across multiple energy carriers is increasingly attracting attention of researchers and policy makers, since it is a prominent means of increasing the overall efficiency of the energy sector. Special attention is attributed to the so-called energy hubs, i.e., clusters of energy communities featuring electricity, gas, heat, hydrogen, and also water generation and consumption facilities. Managing an energy hub entails dealing with multiple sources of uncertainty, such as renewable generation, energy demands, wholesale market prices, etc. Such uncertainties call for sophisticated decision-making techniques, with mathematical optimization being the predominant family of decision-making methods proposed in the literature of recent years. In this paper, we summarize, review, and categorize research studies that have applied mathematical optimization approaches towards making operational and planning decisions for energy hubs. Relevant methods include robust optimization, information gap decision theory, stochastic programming, and chance-constrained optimization. The results of the review indicate the increasing adoption of robust and, more recently, hybrid methods to deal with the multi-dimensional uncertainties of energy hubs.