Electricity prices and tariffs to keep everyone happy: a framework for compatible fixed and nodal structures to increase efficiency

Some consumers, such as householders, are unwilling to face volatile electricity prices, and perceive as unfair price differentiations based on location. For these reasons, nodal prices in distribution networks are rarely employed. However, the increasing availability of renewable resources in distribution grids, and emerging price-elastic behaviour, pave the way for the effective introduction of marginal nodal pricing schemes in distribution networks. The aim of the proposed framework is to show how traditional non-flexible consumers can coexist with flexible users in a local distribution area, where the latter pay nodal prices whereas the former are charged a fixed price, which is derived by the underlying nodal prices. In addition, it determines how the distribution system operator should manage the local grid by optimally determining the lines to be expanded, and the collected network tariff levied on network users, while accounting for both congestion rent and investment costs. The proposed framework is formulated as a non-linear integer bilevel model, which is then recast as an equivalent single optimization problem, by using integer algebra and complementarity relations. The power flows in the distribution area are modelled by resorting to a second-order cone relaxation, whose solution is exact for radial networks under mild assumptions. The final model results in a mixed-integer quadratically constrained program, which can be solved with off-the-shelf solvers. Numerical test cases based on a 5-bus and a 33-bus networks are reported to show the effectiveness of the proposed method.