Profit-based unit commitment models with price-responsive decision-dependent uncertainty

Highlighting the increasing importance of demand elasticity in electricity markets and its impact on the revenues of power generating companies, this paper proposes new profit-based unit commitment models that effectively capture the uncertainty in the willingness-to-pay the price set for the elastic demand. To develop a new revenue scheme for power generating companies, we use a coupling function to model the willingness-to-pay response of the elastic demand as a decision-dependent source of uncertainty. The coupling function reflects how power generating companies’ pricing decisions may influence the market appeal (i.e., the buyer’s willingness-to-pay) and how it affects their revenues. The optimization models are stochastic mixed-integer nonlinear problems with nonconvex continuous relaxations and are not amenable to a numerical solution in their original forms. We devise a convexification reformulation method and derive valid inequalities to strengthen the formulation. We propose a learning framework to parameterize the willingness-to-pay functions and the concept of the value of the decision-dependent solution to quantify the value of the uncertainty modeling approach. Numerical tests on power systems of various sizes, demand portfolios, and price elasticity levels show (i) how the valid inequalities speed up the solution process, (ii) the benefits of properly modeling decision-dependent uncertainty and demand elasticity, and (iii) how the incorporation of decision-dependent uncertainty in demand elasticity can change the power generating companies’ decisions and revenue estimation.