Anthony Downward

On Cournot Equilibria in Electricity Transmission Networks

We consider electricity pool markets in radial transmission networks in which the lines have capacities. At each node there is a strategic generator injecting generation quantities into the pool. Prices are determined by a linear competitive fringe at each node (or equivalently a linear demand function) through a convex dispatch optimization. We derive a set of linear inequalities satisfied by the line capacities that gives necessary and sufficient conditions for the unconstrained one-shot Cournot equilibrium to remain an equilibrium in the constrained network. We discuss the extension of this model to general networks and to lines with transmission losses, and we conclude by discussing the application of this methodology to the New Zealand electricity transmission network.

Supply Function Equilibrium with Taxed Benefits

Supply function equilibrium models are used to study electricity market auctions with uncertain demand. We study the effects on the supply function equilibrium of a tax, levied by the system operator, on the observed surplus of producers. Such a tax provides an incentive for producers to alter their offers to avoid the tax. We consider these incentives under both strategic and price-taking assumptions. The model is extended to a setting in which producers are taxed on the benefits accruing to them from a transmission line expansion (a beneficiaries-pay transmission charge). In this setting, we show how this tax may lead to lower prices in equilibrium.

Electricity retail contracting under risk-aversion

Risk has always been a dominant part of financial decision making in any industry. Recently models, tools and computational techniques have been developed so that we can effectively incorporate risk in optimal decision policies. The focus of this paper is on electricity markets, where much of the inherent risk falls on the retail sector. We introduce a three-stage model of an electricity market where firms can choose to enter the retail market, then enter into retail contracts, and finally purchase electricity in a wholesale market to satisfy their contracts. We explicitly assume that firms are risk-averse in this model. We demonstrate how the behaviour of firms change with risk-aversion, and use the example of an asset-swap policy over a transmission network to demonstrate the importance of modeling risk-aversion in determining policy outcomes.

Modelling counter-intuitive effects on cost and air pollution from intermittent generation

In this paper, we first present a market environment with a conventional two settlement mechanism. We show that when we add some wind generation to the system, the steady-state market conditions yield lower social and consumer welfare and higher use of fossil fuels. We also present results of a counterfactual stochastic settlement market which improves social and consumer welfare after the introduction of new intermittent generation. Thus, we conclude that the choice of market mechanism is a critical factor for capturing the benefits of large-scale wind integration.We also introduce a method to compute analytical equilibria of games in which the payoff functions of players depend on the optimal solution to an optimization problem with inequality constraints.

A multi-stage stochastic optimization model of a pastoral dairy farm

Abstract Pastoral dairy farmers make sequential decisions in the face of long-term environmental uncertainty and price volatility. Decisions made early in the season, such as the number of cows to stock per hectare, can have significant effects later in the season if the farmer is forced to import additional feed to meet the cows’ energy demands during a drought. In this paper, we present POWDer: the milk Production Optimizer incorporating Weather Dynamics. POWDer is a novel multi-stage stochastic program that divides the dairy farming season into weeks and links these weeks by a system of linear dynamics. By applying POWDer to a case farm in New Zealand, we demonstrate POWDer’s promise as a tool that can help participants in the New Zealand dairy industry understand and plan for the challenge of farming in a stochastic world.