  Some consumers, particularly households, are unwilling to face volatile
electricity prices, and they can perceive as unfair price differentiation in
the same local area. For these reasons, nodal prices in distribution networks
are rarely employed. However, the increasing availability of renewable
resources and emerging price-elastic behaviours 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. Flexible users
will pay nodal prices, whereas non-flexible consumers will be charged a fixed
price derived from the underlying nodal prices. Moreover, the developed
approach shows how a distribution system operator should manage the local grid
by optimally determining the lines to be expanded, and the collected network
tariff levied on grid users, while accounting for both congestion rent and
investment costs. The proposed model is formulated as a non-linear integer
bilevel program, 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
both 5-bus and 33-bus networks are reported to show the effectiveness of the
proposed method.
