Nodal and fixed price coexistence in distribution networks with optimal investment planning and tariff design

The aim of the proposed framework is to show how flexible consumers and small generators paying nodal prices can coexist with traditional consumers paying fixed prices at the distribution grid level. The local grid is managed by a distribution network operator who also determines the lines to be built or expanded. A network tariff levied on grid users is optimally determined to ensure the recovery of both fixed and variable investment network costs. The model is structured as a nonlinear integer bilevel program. The upper level represents a long-term network planning problem accounting for investment costs and network tariffs. The lower level is a market clearing problem, which considers the upper level investment decisions, and determines the cleared quantities and the distribution nodal prices. These values are used in turn by the upper level problem to determine the fixed price paid by traditional consumers and to ensure the recovery of the overall investment costs. The bilevel model is then recast as a mixed-integer quadratically constrained problem by using integer algebra and complementarity relations. The power flows at the distribution grid level are modelled by using a second-order cone relaxation. Numerical tests based on a 18-bus low-voltage distribution network show that an increase of demand flexibility can be beneficial also for traditional consumers by triggering a reduction of fixed prices, and can mitigate the subsidising effect between them. Moreover, the optimal network planning shows that a significant welfare increase can be obtained, while ensuring the recovery of both fixed and variable costs through congestion rent and network tariffs levied on grid users.