Bi-level retail pricing scheme considering price-based demand response of multi-energy buildings

•A bi-level retail pricing model is proposed for the distribution system operator.•An optimal energy management model is established for multi-energy buildings.•Both linearization and relaxation methods are applied to reformulate the model.•The Dantzig-Wolfe decomposition is applied to solve the market equilibrium model. Multi-energy buildings can help the consumers to achieve more efficient energy consumption and offer more flexible demand response. However, since the demand response and retail pricing affect each other, an equilibrium based retail pricing scheme should be developed where the energy costs of the consumers can be reduced and more profits can also be earned by the retailer at the same time. Therefore, this paper proposes an optimal bi-level retail pricing scheme for the retailer and consumers of the multi-energy buildings to perform the price-based demand response program. In the lower-level, the optimal building energy management model considering the thermal dynamic and multi-energy conversion is established to minimize the energy costs, which ensures the benefits of consumers and also represents the dynamic response characteristic of the multi-energy building; in the upper-level, the optimal pricing strategy of the retailer is modelled to maximize its profit, and the stochastic AC power flow is applied to deal with the uncertain output of the renewable energy sources. By reforming the bi-level structure, linearizing the price-load coupled objective, and relaxing the power flow with the second-order cone, the modified market equilibrium model is solved by the Dantzig-Wolfe decomposition in a distributed way, which can protect the privacy of different players and deal with the undifferentiable integer variables caused by the reformulation. The simulation results demonstrate the efficacy of the proposed retailing pricing scheme and distributed solution algorithm.