The stability of power system markets

Abstract

Market equilibrium conditions can be derived from more general dynamic equations describing the marketplace. Dynamic equations provide insights into the behavior and stability of markets which are not available from static models. For example, markets with a single supplier with declining linear costs (economies of scale) may or may not be stable, depending on specific cost characteristics. Markets with more than one supplier with declining linear costs are always unstable. This paper illustrates a situation where the removal of congestion makes a market unstable.

Feedback, competition and stochasticity in a day ahead electricity market

“…This condition expressing the optimal behavior of a competitive producer in a deregulated market is customarily used in the literature (see Alvarado (1999) and Liu (2006)). Collaborative bidding and network effects could also affect the players' decisions, thus leading to a different condition for optimality.…”

“…Basically, two production technologies dominate the Danish electricity market, which is the main focus of this article: conventional thermal production and wind power, which account for, respectively, about 85% and 15% of the market. Generally, the existing literature on the subject (for instance see Martini et al (2001), Yu et al (1998), Alvarado (1997)) considers quadratic cost functions as a good approximation of the costs of a generator using thermal plants. Furthermore, it is known that for wind production plants the running cost is basically null with the exception of the maintenance and the startup costs.…”

“…With Alvarado (1999) and Liu (2006) as sources of inspiration, the Cournot competition is modeled as a closed loop system, where the feedback signal is the price (which is always made public in restructured energy markets) while the control signals are the individual bids of the generators, that is quantities. The structure of the energy market, which is divided into hourly bidding rounds, suggests discrete time as the straightforward framework.…”

“…As a matter of fact, the period to period interrelation between the bids and the periodicity in the demand characteristic represent just two straightforward arguments substantiating the importance of modeling the energy market as a dynamic system. Nevertheless, as of now, little of the existing work has undertaken this direction; among the few exceptions Alvarado (1997), Liu (2006) and Conejo et al (2002).…”

Bidding Strategies in Oligopolistic Dynamic Electricity Double-Sided Auctions

“…Alvarado [2] has studied the stability of power system markets by means of eigenvalues technique. He studies the stability of several market structures, where only one of them is of interest to us: "A market with m suppliers and n elastic consumers".…”