Our research uses mathematical modelling, optimization and statistical tools to comprehend modern electricity markets such as the NZEM, and to analyze and develop methods for efficient generation schemes and demand-side participation.

In 2025 electricity production from wind power should constitute nearly 50 % of electricity demand in Denmark. In this paper we look at optimal expansion of the transmission network in order to integrate 50 % wind power in the system, while minimising total fixed investment cost and expected cost of power generation. We allow for active switching of transmission elements to eliminate negative effects of Kirchhoffs voltage law. Results show that actively switching transmission lines may yield a better utilisation of transmission networks with large- scale wind power and increased wind power penetration. Furthermore, transmission switching is likely to affect the optimal line capacity expansion plan.

We consider the application of Dantzig-Wolfe decomposition to stochastic integer programming problems arising in the capacity planning of electricity transmission networks that have some switchable transmission elements. The decomposition enables a column-generation algorithm to be applied, which allows the solution of large problem instances. The methodology is illustrated by its application to a problem of determining the optimal investment in switching equipment and transmission capacity for an existing network. Computational tests on IEEE test networks with 73 nodes and 118 nodes confirm the efficiency of the approach.

This talk covers pricing of contingent claims, such as financial options, using discrete time stochastic programming under multi-period scenario trees. It is well known that the absence of arbitrage profits in the state space is equivalent to the existence of a martingale probability measure when there are no transactions costs. When such trees are utilized in stochastic programming in pricing contingent claims defined on the state space, the problem reduces to one of solving a generalized moment problem at each node. Appealing to well-known bounding results from the literature, I propose a simplicial upper bounding procedure based on recursive backward dynamic programming. This serves to formalize the known results as well as to provide extensions. The results are also generalized to the case of when proportional transactions costs are present for trading. With increased transactions costs, it is shown why arbitrage-free multi-period (state price) scenario trees are easier to generate. Geometric interpretations and preliminary computational results will be presented.

The EU ETS, launched in 2005, is the world's first international cap-and trade system governing CO2 emissions. The consideration of carbon, its pricing and business implications has become key for all actors in the European power sector, from board level to the trading floor. As well as providing a brief background and overview of the EU ETS and European power market(s), this talk will provide a personal experience of the changing impact of the ETS on the pricing of power, investment decisions, trading, hedging and analysis. We will also touch briefly on some key trends driving developments within the EU energy complex, of which CO2 forms an integral part.

Security of supply is a frequently addressed concern in electricity markets such as the NZEM. Sufficient investment in generation is needed to ensure the security of electricity supply in such markets yet, electricity generators are risk averse with respect to such large investments and governments mindful of gold-plating the system and/or interfering in deregulated markets. We will develop a model that employs coherent risk measures to reflect a generating firm's risk aversion level and recommend under an assumed stochastic process for the price of electricity and perhaps another stochastic process for fuel cost, if that firm should invest in building a generation plant.

This project aims to extend the existing EPOC models and build new models that address the question of optimizing revenue for a hydro-electric generator whose actions influence the price of electricity. Such generators are often major generators. As their offer policy influences the outcome of the dispatch, hence the price of electricity, they cannot observe price as an exogenous process.

Presentation to Dean's Lecture Series, University of Auckland School of Engineering.

Presentation to ONS Workshop, Rio de Janeiro, August 17, 2011.

Talks now available for download

Talks now available for download