Since the 1990s, widespread introduction of central (wholesale) electricity markets has been seen across multiple continents, driven by the search for efficient operation of the power grid through competition. The increase of renewables has made significant impacts both on central electricity markets and distribution-level grids as renewable power generation is often connected to the latter. These stochastic renewable technologies have both advantages and disadvantages. On one hand they offer very low marginal cost and carbon emissions, while on the other hand, their output is uncertain, requiring flexible backup power with high marginal cost. Flexibility from end-prosumers or smaller market participants is therefore seen as a key enabler of large-scale integration of renewables. However, current central electricity markets do not directly include uncertainty into the market clearing and do not account for physical constraints of distribution grids. In this paper we propose a local electricity market framework based on probabilistic locational marginal pricing, effectively accounting for uncertainties in production, consumption and grid variables. The model includes a representation of the grid using the lindistflow equations and accounts for the propagation of uncertainty using general Polynomial Chaos (gPC). A two-stage convex model is proposed; in the day-ahead stage, probability distributions of prices are calculated for every timestep, where the expected values represent the day-ahead (spot) prices. In the real-time stage, uncertainties are realized (measured) and a trivial calculation reveals the real-time price. Through four instructive case-studies we highlight the effectiveness of the method to incentivize end-prosumers' participation in the market, while ensuring that their behavior does not have an adverse impact on the operation of the grid.
Austnes et al. (Tue,) studied this question.