A market-oriented stochastic optimization framework and its application in the energy domain

In this paper we present a novel market-oriented stochastic optimization framework, which can be used to optimize the unit commitment of a portfolio of distributed generation units (DG) and demand response resources (DRR) on a 24 h base. Key contributions of this work is the explicit incorporation of uncertainties in demand resp. supply curves and their corresponding mapping to market prices. The framework is based on the theory of competitive multi commodity markets in which a market operator utilizes a real-time price signal to indirectly adjust the commodity (quantities of energy) allocation of his portfolio of price-elastic DG units and DRR. We extend this approach to incorporate uncertainties in commodity allocations (for consumers) as well as production schedules (for producers), which are modeled as independent probability density functions (PDFs) over the quantity of each commodity. The aggregated PDFs of the commodity quantities are mapped to the price domain using a piece-wise linear approximation of the producer´s/ consumer´s gain functions. The resulting stochastic price signal holds additional incentives for DRR and DG units to reserve flexibility for periods of high allocation uncertainties. Thus additional to finding an optimal allocation schedule the pricing mechanism also allows the balancing of demand/ supply flexibility with the risk of uncertain demand/ supply deviations.