Supply function equilibria, in which firms offer a schedule of prices and quantities, are a natural way to describe the behaviour of a spot market for electricity. We study the equilibrium behaviour in the asymmetric case, when firms differ both with regard to costs and capacities. We look for a strong form of Nash equilibria in which, given the other players' supply functions, optimal profits are achieved for every demand realisation. We propose a novel method to find asymmetric supply function equilibria, using piecewise linear approximations and a discretization of the demand distribution. We show that this approach is effective in practice and explore the extent to which mutiple equilibria will occur.

This paper derives a Supply Function Equilibrium (SFE) of a pay-as-bid auction (discriminatory auction), such as the balancing market for electric power in Britain. It is shown that a SFE always exists if the hazard rate of the perfectly inelastic demand is monotonically decreasing and marginal costs are non-decreasing. With demand following a Pareto distribution of the second kind, the SFE of a pay-as-bid auction is compared to the SFE of a uniform-price auction, the auction form in most electricity markets. The demand-weighted average price in the former is found to be (weakly) lower than in the latter.

The concept of a supply function equilibrium (SFE) has been widely used to study generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that the presence of pivotal suppliers reduces the set of supply function equilibria. We show that the size of the equilibrium set depends on observable market characteristics such as the amount of industry excess capacity and the load ratio (ratio of minimum demand to maximum demand). As the amount of excess capacity falls and/or the load ratio rises, the set of supply function equilibria becomes smaller; the equilibria that are eliminated are the lowest-priced, most competitive equilibria.

We consider a wholesale electricity market model with general networks, transmission losses and strategic producers. A previous work by Escobar and Jofre (2005) shows how regulation mechanisms such as the case when prices correspond to the Lagrange multipliers of a centralized cost minimization program allows the producers to charge significantly more than marginal price. In this paper we derive an optimal regulation mechanism for that type of networks, and compare its performance with the Bayesian version of the "price equal to Lagrange multiplier" one.

One of the attractions of supply-function offers in electricity pool markets is the possibility that they might yield optimal profits for generators for every realization of (uncertain) demand. A supply-function equilibrium (SFE) in the strong sense is defined by a supply function for each generator that has this property assuming fixed supply functions for the other generators. (A weak SFE has the property that each agent selects a supply function that maximizes expected profit.) There has been much recent attention on deriving strong SFEs in single-node markets, and some results demonstrating the existence of weak SFEs in transmission networks with losses. In this talk we examine the construction of a strong SFE in a transmission network with losses, and show why this is not possible except in some special circumstances.

We will describe the construction of supply function equilibria over the New Zealand electricity network using fictitious play. We will present and discuss computational results and the nature of equilibria arising from our experiments.

The Chilean power market design is based on a mandatory Pool with audited costs and financial bilateral contracts. The wholesale spot market is opened only to generators who exchange energy at hourly marginal costs and capacity at a power price. Based on the Peak Load Pricing theory, power (capacity) contribution of generators have been recognized as a commodity paid by the users. In the past, these payments were associated with adequacy and security attributes of generation units. The new changes in the electricity law restrict the concept of capacity payments to the system adequacy contribution of each unit. In the new concept, security aspects are being treated through ancillary services. This work proposes a capacity payment scheme that recognizes primary energy availability, failures, maintenance of each unit, and transmission system constraints. The approach uses historical information and a Monte-Carlo simulation scheme. Distributed generation is explicitly considered in the proposal. The proposed model is applied for the Chilean system. Results show the effects and price signals for conventional and DG units in different hydrology and natural gas availability conditions.

Cournot models have been used extensively to simulate both the operation of hypothetical electricity markets and the effects of hypothetical changes to existing electricity markets. However, very little work has been undertaken in discovering how successful these models were at estimating future price behaviour after either the markets have begun operation or the changes have been implemented. We have calibrated a Cournot model with real market data from Australia's National Electricity Market, treating two of the crucial inputs required by a Cournot model, the elasticity of demand and the contract level, as exogenous parameters, to be estimated so as to match real market behaviour. A stochastic spot price time series model is then fitted to model the residual price movements not captured by the Cournot model. The approach has obvious limitations, and our study could be considerably refined, but the combination provides a practical tool for spot price forecasting, allowing us to estimate the likely effect of varying fundamental market parameters on the realistic market price patterns.