Price Adjustment in Price-based Coordination Using Quadratic Approximation

Authors:

Wenzel, Simon; Paulen, Radoslav; Krämer, Stefan; Beisheim, Benedikt; Engell, Sebastian

Conference:

26th European Symposium on Computer Aided Process Engineering

http://dx.doi.org/10.1016/B978-0-444-63428-3.50037-0

Abstract:

Site-wide allocation of shared resources among the units of (partially) autonomous plants can be realized by price-based coordination. In an iterative procedure, a central site-coordinator adjusts the transfer prices for shared resources based on the network (im)balance until the equilibrium price λ∗ is found which assures the achievement of network balance. This process is known as tâtonnement of the exchange (Uzawa, 1960) and has the benefit of keeping local cost information of the plants confidential. One of the drawbacks of the tâtonnement process is its slow rate of convergence. In addition it is very sensitive to the choice of the step size parameter in the price update. In this contribution, we propose a novel price update based on quadratic approximation of the residual of a network of production plants with strictly convex cost functions. We perform simulation studies for an academic example and an industrial case study of balancing steam networks in an integrated petrochemical production site to show the much improved rate of convergence in comparison to classical subgradient price updates.