Continuous-time Marginal Pricing of Power Trajectories in Power Systems

TL;DR

This paper develops a continuous-time economic dispatch model for power systems that incorporates ramping constraints, deriving a marginal price that accounts for inter-temporal resource limitations, especially relevant with increasing renewable variability.

Contribution

It introduces a novel continuous-time formulation of power dispatch with ramping constraints and derives a new marginal pricing expression using Euler-Lagrange equations.

Findings

Derived marginal price expression using Euler-Lagrange equations.

Price better reflects market value with significant ramping constraints.

Addresses increased importance of ramping due to renewable variability.

Abstract

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.