Empowering Prosumers: Incentive Design for Local Electricity Markets Under Generalized Uncertainty and Grid Constraints

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. The lindistflow equations combined with gPC allows to derive a convex, second-order cone model, ensuring global optimality. A two-stage model is proposed; in the day-ahead stage, probability distributions of prices are calculated for every timestep, where the expected values represents 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. The proposed methodology significantly reduces the needs for performing real-time calculations, ensuring its practicality and efficiency in real-world applications.