Continuous-time Marginal Pricing of Power Trajectories in Power Systems
  In this paper we formulate of the Economic Dispatch (ED) problem in Power Systems in continuous time and include in it ramping constraints to derive an expression of the price that reflects some important inter-temporal constraints of the power units. The motivation for looking at this problem is the scarcity of ramping resources and their increasing importance motivated by the variability of power resources, particularly due to the addition of solar power, which exacerbates the need of fast ramping units in the early morning and early evening hours. We show that the solution for the marginal price can be found through Euler-Lagrange equations and we argue that this price signal better reflects the market value of power in the presence of significant ramps in net-load. 
Anna Scaglione
math.OC