Real-time Prices in an Entropic Grid

G. Wang and M. Negrete-Pincetic and A. Kowli and E. Shafieepoorfard and S. Meyn and U. V. Shanbhag

Invited lecture at the CDC 2011 session on Smart Grid Planning - Market, Pricing, and Security
Organizers: Anu Annaswamy and Jakob Stoustrup
Co-organizers: Michael Caramanis and John Baillieul

Abstract: If you talk to a control theorist today about the road to achieve an efficient, reliable, and affordable electricity supply you will most likely be told that real-time prices will be a part of its realization. Perhaps this is true. However, we argue that appropriate design using economic models that can capture the emerging physical realities is a key requirement for achieving a reliable, and "smart" electrical grid.

In a few years, smart meters and wind farms may be regarded as another bridge to nowhere unless we create the right architecture to make use of these resources.

To capture the potential pitfalls of real-time prices, we present an extension of our earlier work on dynamic markets to general network settings, allowing for more general constraints on generation and transmission. We conclude in wide generality that in the economic ideal of the competitive equilibrium, the standard results follow - the equilibrium is efficient, and average prices coincide with average marginal cost. However, these conclusions hold only on average. More importantly, we find that in the competitive equilibrium,

  1. Prices can be negative,
  2. Prices can go well above the choke up price (the maximum price consumers are willing to pay in a static market model)
  3. The variance of the price may be very large, but decreases with increasing demand response.

We illustrate these finding through numerical experiments.

See also the recent survey Dynamic Competitive Equilibria in Electricity Markets - bibliographic information can be found below.

Survey & Panel Lecture, PES, July, 2011

Presentation, New England ISO, July, 2010

Newton Institute Tutorial and Panel Lecture, May, 2010 (see also the Cambridge website)


This paper explains the exotic behavior of prices seen throughout the world. For example, in Texas:

Texas Prices

Wall Street Journal, February 7, 2011, Texas to Probe Rolling Blackouts: Texas officials have ordered an investigation into rolling blackouts that struck the state's electric grid last week, including whether market manipulation played a role along with harsh weather in disrupting natural-gas and electricity supplies to millions of people.

and, in Australia:

Tasmania & Victoria Prices

Tasmania Map  

Power prices in markets around the world can appear entirely irrational. In 2007, prices for power reached $10,000 Aus. in Victoria, many times greater than the ususal value near $50. At the same time, prices crashed to a negative value in Tasmania (-$1,000 Aus).

Similar high prices are seen today in European and North American markets.






Title = {Real-time Prices in an Entropic Grid},
Author = {G. Wang and M. Negrete-Pincetic and A. Kowli and E. Shafieepoorfard and S. Meyn and U. V. Shanbhag},
Note = {Submitted to {2011 IEEE CDC}},
Year = {2011}}

Title = {Dynamic Competitive Equilibria in Electricity Markets},
Author = {Wang, G. and Negrete-Pincetic, M. and Kowli, A. and Shafieepoorfard, E. and Meyn, S. and Shanbhag, U.},
Editor = {A. Chakrabortty and M. Illic},
Publisher = {Springer},
Booktitle = {Control and Optimization Theory for Electric Smart Grids},
Year = {2011}}

Title = {A Control Theorist's Perspective on Dynamic Competitive Equilibria in Electricity Markets},
Address = {Milano, Italy},
Author = {G. Wang and A. Kowli and M. Negrete-Pincetic and E. Shafieepoorfard and S. Meyn},
Booktitle = {Proc. 18th World Congress of the International Federation of Automatic Control (IFAC)},
Year = {2011}}

Title = {Intelligence by Design for The Entropic Grid},
Author = {M. Negrete-Pincetic and S.P. Meyn},
Booktitle = {IEEE PES 11: Power Energy Society General Meeting},
Year = {2011}}

Title = {The Value of Volatile Resources in Electricity Markets},
Author = {Meyn, S. and Negrete-Pincetic, M. and Gui Wang and Kowli, A. and Shafieepoorfard, E.},
Booktitle = CDC2010,
Pages = {1029 -1036},
Year = {2010}}

Author = {I.-K. Cho and S. P. Meyn},
Title = {Efficiency and marginal cost pricing in dynamic competitive markets with friction},
Journal = {Theoretical Economics},
Number = {2},
Pages = {215-239},
Volume = {5},
Year = {2010}}

Author = {Cho, I.-K. and Meyn, S. P.},
Note = {Submitted for publication, {SIAM J. Control and Optimization.}},
Title = {A Dynamic Newsboy Model for Optimal Reserve Management in Electricity Markets},
Year = {2009}}

Author = {Chen, M. and Cho, I.-K. and Meyn, S.P.},
Journal = {Automatica},
Month = {August},
Pages = {1267-1281},
Title = {Reliability by design in a distributed power transmission network},
Volume = {42},
Year = {2006}}

Title = {Efficiency and marginal cost pricing in dynamic competitive markets with friction},
Author = {Cho, In-Koo and Meyn, S.},
Journal = {Decision and Control, 2007 46th IEEE Conference on},
Month = {Dec.},
Pages = {771-778},
Year = {2007}}

Title = {The dynamics of the ancillary service prices in power networks},
Author = {Cho, I.-K. and Meyn, S. P.},
Booktitle = {Proceedings of the 42nd IEEE Conference on Decision and Control},
Month = {December 9-12},
Pages = {2094- 2099},
Volume = {3},
Year = {2003}}