ML-Enhanced Bilevel Optimization for Real-Time Electricity Pricing
摘要
This paper introduces a novel approach to electricity pricing that combines a Bi-Level optimization model with Machine Learning techniques for forecasting uncertain photovoltaic generation. The transition to sustainable energy systems indeed necessitates sophisticated pricing strategies to balance the interests of aggregators and prosumers—individuals who both consume and produce renewable energy. In our Bi-Level framework, the aggregator (leader) sets dynamic electricity prices aiming to maximize profit while anticipating the reactions of a residential prosumer (follower), who seek to minimize his energy costs and discomfort from load adjustments. The study focuses on dynamic pricing schemes, particularly Real-Time Pricing, which align electricity prices with real-time market conditions to incentivize demand-response behaviors. Given the variability in photovoltaic generation, accurate day-ahead forecasts are crucial. We employ Machine Learning techniques to predict photovoltaic power production, integrating these forecasts into the Bi-Level model using a “predict, then optimize" approach. This approach ensures that the optimization remains computationally tractable, while effectively incorporating uncertainty. To manage the high complexity inherent in Bi-Level formulations, the model is first transformed into a single-level structure by exploiting the Karush-Kuhn-Tucker optimality conditions of the lower-level problem. An exact linearization technique is used to deal with the bi-linear terms in the leader’s objective function, while the non linearity of Karush-Kuhn-Tucker complementarity conditions is overcome by employing SOS-1 constraints. An extensive experimental phase is conducted using a real-world case study to validate the proposed methodology and to quantify the impact of the forecasting errors on the supplier’s strategy.