Convex hull pricing in local energy markets

The increasing decentralization of power production in electricity networks (linked to the increasing share of distributed renewable resources, such as solar panels) sets up new challenges and, among them, the need for coordination between the transmission system operator and the distribution system operator. The potential of this coordination offers not only the opportunity to optimize the grid balance at a broader level, but also the opportunity to optimize the choice of the prices more globally, which is the subject of this work. While basing our model on an second order cone (SOC) relaxation of the optimal power flow (OPF) problem, a specific dual function optimization method is studied (namely, the "level method") for the purpose of the computation of one of the pricing scheme (namely, the convex hull price) and different pricing approaches for real and reactive power are then analyzed on an actual, country-scale dataset (provided by SmartNet). Our analysis reveals that the level method should be disregarded when the size of the dual space is large but that the convex hull price is still of interest since an approximate of it can give a lower uplift than other pricing schemes. More broadly, on the analyzed scenarii, the uplifts required are negligible compared to the profits generated.