Efficient market-clearing prices in markets with nonconvexities

Abstract

This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf (1994).Economics, Equilibrium Pricing; MIP models of markets, MIP Applications

Pumped storage in systems with very high wind penetration

“…If storage is a price taker then it should follow that in a sufficiently competitive market, the privately owned storage gives the same effect as that operated for system benefit. The work done in O'Neill et al (2005), Sioshansi et al (2008) and has shown that in markets where there are non-convexities that cannot be priced properly, as would be the case with storage, then the welfaremaximising benefits of storage may not be fully realised. Storage does not bid into the market here, but is used to reduce overall system operating costs.…”

Equilibrium prices supported by dual price functions in markets with non-convexities

“…that the production possibility set displays constant or decreasing returns to scale. When we on the other hand, have increasing returns to scale the pricing test for optimality might fail, and it is easy to construct examples showing this, for instance by introducing activities with start up costs (a very simple example is provided in O'Neill et al 2002). With the lack of a pricing test, Scarf introduces as an alternative a quantity test for optimality.…”

“…In such markets, the non-convexities arise from start-up and shut-down costs of power plants, and minimum output requirements that must be fulfilled in order to run certain plants (see for instance O'Neill et al (2001O'Neill et al ( , 2002 or Hogan and Ring (2003)). Moreover, non-convexities in a market with uniform linear prices may contribute to and legitimate strategies like "hockey stick" bidding, which may have considerable redistribution effects (Oren (2003)).…”

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

“…This is necessary to prevent players from leaving the market. As discussed by O'Neill et al (2005), Morales et al (2012), and Wang et al (2012); uplift payments can result from using incomplete characterizations of the system in the clearing model. Such characterizations can arise, for instance, in the presence of nonconvexities and stochasticity.…”

“…(2001). Pricing issues arising in deterministic clearing formulations have been explored by Wang et al (2012), Galiana et al (2003), andO'Neill et al (2005).…”