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.

Auctions of divisible-goods occur in a number of settings, the most well-known being electricity pool-markets. There are two common payment mechanisms for these auctions, one where a uniform price is paid to all suppliers, and an alternative that adopts a discriminatory, or pay-as-bid, price. Under the assumptions that demand is uncertain and costs are common knowledge, we study supply-function equilibria in the pay-as-bid auction using the concept of market-distribution functions. We show that pure-strategy Nash equilibria typically do not exist in this setting, and derive mixed-strategy equilibria of various types.

In April 2009 the New Zealand Commerce Commission released a review of the New Zealand Electricity Market (NZEM). This review, commonly referred to as the Wolak report, concluded that there was evidence of exercise of market power in the NZEM and was followed by a ministerial review of the NZEM. Both the Wolak report and the market review suggested a number of structural improvements for the NZEM. The likeliest structural change, suggested by both reviews, is a number of asset swap and divestiture options. We will present a brief review of the NZEM and the background to these suggested changes. We will then examine these suggestions in the frame work of simple Cournot models in presence of changing costs and line constraints. We will demonstrate that for our simple examples, these structural changes will achieve the opposite of what was intended.

The standard scenario tree for multi-stage stochastic programs assumes that forecasts of uncertain data are unbiased. We found a counterexample to this assumption in a study of the effect of uncertain natural gas prices on optimal fuel consumption for electricity generation in the U.S. The underlying optimization model is a regionally and temporally aggregated transshipment model of the acquisition, transportation and storage of coal and natural gas along with electricity generation and transmission to meet fixed demands over a medium-term horizon. In an instance based on historical data, we devised a rolling two-stage procedure to compare the optimal flows under natural gas cost information as it became available publicly over time to the flows that were optimal in hindsight. The solution for uncertain costs generated a higher proportion of electricity from natural gas than the hindsight solution did and it also matched the actual historical generation mix more closely. We examine three possible explanations for the observed higher utilization of natural gas under uncertainty. Evidence based on optimality conditions and data analysis suggests that, in this instance, it was mainly attributable to expectations of low natural gas costs that were contradicted by later events. We conclude that forecast bias in stochastic programming merits further study.

Electricity price series can be modelled as a combination of stochastic and deterministic factors. STEPS estimates New Zealand electricity spot prices as an autoregressive function of hydroelectric reservoir levels, and hydroelectric reservoir releases as a function of inflows and spot prices. A web-accessible Python implementation combines these two models and historical water inflows to predict future electricity price sequences.

International Power is a independent power generation company with interests in over 40 power stations and some closely linked businesses around the world. The markets in which we operate in consist of both contractual PPA's as well more conventional merchant markets. The UK is a significant market for us where we have several assets. This seminar will briefly describe the physical UK Power market which is quite different to the SMP markets that prevail in Australia and New Zealand, and also describe the impact of the European Union Emissions Trading Scheme has on the trading of our stations. Each of our assets in the UK have unique features which to which we have applied optimisation techniques which feed into the Trading, Risk Management and Finance functions. Lastly we apply operations research and financial engineering techniques to many of the other valuation and analysis problems that the UK and other regions face and some examples are described.

The Clutha system consists of three lakes with controlled flow, and two power stations witha total of 12 units and maximum capacity of 750MW. This presentation will cover the methods used to create a unit commitment model, which optimizes generator revenue over a week.

We consider the problem of optimizing a supply function bid into a discriminatory auction in which each agent is paid their bid price on each increment of offered capacity. Such a pay-as-bid (PAB) auction was adopted in the England and Wales electricity market under the NETA trading arrangements which replaced the old uniform-priced auction. There has been some skepticism about the efficacy of PAB auctions in comparison with uniform-priced auctions, as it is conjectured that in the former auction agents will simply bid their offer prices up to an anticipated clearing price. In this talk I will show how PAB auctions can be studied using market distribution functions. These can be used to derive optimality conditions for each agent, and to compute Nash equilibria in supply functions. In most realistic cases, there are no pure-strategy equilibria in this game. In the absence of capacities and price-caps, there are infinitely many mixed strategy equilibria, which become uniquely determined when generators have limited capacities and are subject to a price cap. (joint work with Eddie Anderson, UNSW)

A miniature model of SPD exists with 18 nodes. This talk will outline the implementation of the SPD software for a full scale problem with a focus on risk and reserve in the system.

The Electricity Commission was established in September 2003 to regulate and oversee the operation of the electricity industry and markets (wholesale and retail) in accordance with the Electricity Act and government energy policy. A significant focus of the Commission's modelling group is to support the work arising from Part F of the Electricity Governance Regulations and Rules (Transport Rules), in particular grid investment. This presentation will briefly review the modelling projects underway at the Commission. Attention will then turn to presenting the structure and operation of the Commission's generation expansion model (GEM). GEM is a mixed integer program and was used to develop the grid planning assumptions that underpin the evaluation of proposed grid investments. GEM has also been used recently to support work by MED and EECA on the energy strategy and the energy efficiency and conservation strategy, respectively.

This talk is concerned with characterizing a set of conditions which ensure the existence of an uncongested Cournot equilibrium over an electricity network. Our Cournot model consists of strategic generators and linear fringes over a pool market. When the transmission network is radial, we derive necessary and sufficient conditions on the line capacities, ensuring that the unconstrained Cournot equilibrium remains an equilibrium. These conditions form a convex polyhedral set, which allows for optimization of resources while ensuring competitive play.

Electricity distributors such as Transpower and Vector are among the regulated industries in NZ and have a cap on their annual revenue. Hence electricity distributors seek a policy of setting their fixed, variable and peak charges so as to meet a target revenue and discourage peak consumption. Peak consumption leads to (future) investment cost that is to be avoided if possible. In order to discourage peak consumption, they need a model for consumer behaviour. We will consider peak shaving and peak shifting models for consumers in a distribution network and analyze the distributor's revenue optimization problem as a 2 stage leader-follower game. This project will be extended to consider coincident peak charges (where more than a single major consumer is involved,) stochastic spot prices of electricity, and the network effects (i.e. the location of the consumers).

Spot market for electricity is treated as an auction of shares, where generators submit their supply function and consider demand as uncertain. This paper proposes a procedure to estimate the structural parameters of this model, accounting for asymmetry across bidders, and compare auction outcomes under pas-as-bid or uniform-price format.

This paper analyses the strategic behaviour of two competing hydropower plants located along the same river. In this situation an externality arises, as any amount of water released by the upstream plant to produce power ends up in the downstream plant's reservoir, expanding the latter's generation capacity. The paper studies the conditions under which the upstream generator has the strategic incentive to reduce its own production level, in order to constrain the productive capacity of its downstream competitor. It is shown that such incentive depends on the reservoir levels and on the state of demand. First, the equilibrium production levels vary non-monotonically and discontinuously with the stock of water in the reservoirs. Second, the upstream plant benefits most from reducing its production during off-peak periods, since it is then able to exert more market power when the peak period comes. The paper also studies the incentives of generators to collude, and finds that generators benefit less from collusion when reservoir levels are low.

We propose an alternative way of risk modeling in two-stage stochastic programming. Rather than heading for first-stage solutions minimizing quantifications of risk, we introduce a stochastic benchmark and identify those first-stage solutions leading to total costs that are "acceptable" with regard to the benchmark. Stochastic dominance provides a way for making this "acceptability" mathematically rigorous. A stochastic optimization problem arises when minimizing an objective function over the set of "acceptable" points. We discuss the structure of these optimization problems, propose a decomposition algorithm for their solution in case the underlying probability spaces are finite, and report some first computational results at instances from power optimization.

We propose an alternative way of risk modeling in two-stage stochastic programming. Rather than heading for first-stage solutions minimizing quantifications of risk, we introduce a stochastic benchmark and identify those first-stage solutions leading to total costs that are "acceptable" with regard to the benchmark. Stochastic dominance provides a way for making this "acceptability" mathematically rigorous. A stochastic optimization problem arises when minimizing an objective function over the set of "acceptable" points. We discuss the structure of these optimization problems, propose a decomposition algorithm for their solution in case the underlying probability spaces are finite, and report some first computational results at instances from power optimization.