Geoffrey Pritchard

A Single-Settlement, Energy-Only Electric Power Market for Unpredictable and Intermittent Participants

We discuss a stochastic-programming-based method for scheduling electric power generation subject to uncertainty. Such uncertainty may arise from either imperfect forecasting or moment-to-moment fluctuations, and on either the supply or the demand side. The method gives a system of locational marginal prices that reflect the uncertainty, and these may be used in a market settlement scheme in which payment is for energy only. We show that this scheme is revenue adequate in expectation.

Hydroelectric reservoir optimization in a pool market

Abstract.For a price-taking generator operating a hydro-electric reservoir in a pool electricity market, the optimal stack to offer in each trading period over a planning horizon can be computed using dynamic programming. However, the market trading period (usually 1 hour or less) may be much shorter than the inherent time scale of the reservoir (often many months). We devise a dynamic programming model for such situations in which each stage represents many trading periods. In this model, the decision made at the beginning of each stage consists of a target mean and variance of the water release in the coming stage. This decomposes the problem into inter-stage and intra-stage subproblems.

Exact results on manipulability of positional voting rules

We consider 3-candidate elections under a general scoring rule and derive precise conditions for a given voting situation to be strategically manipulable by a given coalition of voters. We present an algorithm that makes use of these conditions to compute the minimum size M of a manipulating coalition for a given voting situation. The algorithm works for any voter preference model — here we present numerical results for IC and for IAC, for a selection of scoring rules, and for numbers of voters up to 150. A full description of the distribution of M is obtained, generalizing all previous work on the topic. The results obtained show interesting phenomena and suggest several conjectures. In particular we see that rules “between plurality and Borda” behave very differently from those “between Borda and antiplurality”.

Financial transmission rights in convex pool markets

This paper studies financial transmission rights in electricity pool markets with nodal pricing. We prove that simultaneous feasibility entails revenue adequacy in a general framework of convex optimization, and show by counterexample as to how this result might fail in the absence of convexity.

Offer Stack Optimization in Electricity Pool Markets

We consider a generator making offers of energy into an electricity pool market. For a given time period, it must submit an offer stack, consisting of a fixed number of quantities of energy and prices at which it wants these quantities dispatched. We assume that the generator cannot offer enough power to substantially affect the market price, so the optimal response would be to offer energy at marginal cost. However, the market rules do not permit an arbitrary function, so the problem is to find an offer stack approximating marginal cost in a way that maximizes its profit. We give optimality conditions for this problem and derive an optimization procedure based on dynamic programming. This procedure is illustrated by applying it to several examples with different costs of production.

Market Offering Strategies for Hydroelectric Generators

This paper considers the problem of offering electricity produced by a series of hydroelectric reservoirs to a pool-type central market. The market model is a simplified version of the New Zealand wholesale electricity market, with prices modelled by a first-order Markov process. The demand for electricity is not explicitly modelled. The hydroelectric generator is assumed to be unable to influence market prices (i.e., to be a price-taker). We discuss the resulting stochastic dynamic program, methods for its solution, and the explicit optimal offer curves that it produces. It is shown that the utility function is monotone increasing with respect to both reservoir level and current price; however, the optimal offer curves need not be monotone. This is shown by example. Numerical results are provided.

Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour

We consider the problem of manipulation of elections using positional voting rules under impartial culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters who must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This permits a comparative analysis of the asymptotic (large-population) manipulability of the various rules. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed three- and four-candidate cases.

On financial transmission rights and market power

This paper studies financial transmission rights in electricity pool markets with nodal pricing, when these rights are to be allocated by an auction mechanism. A market distribution function approach is used to investigate the effects on electricity offering behaviour when participants hold financial transmission rights, and the implications of this for the auction design are discussed.

Nonparametric Estimation of Market Distribution Functions in Electricity Pool Markets

The market distribution function is a probabilistic device that can be used to model the randomness in dispatch and clearing price that generators in electricity-pool markets must take account of when submitting offers. We discuss techniques for estimating the market distribution function, and ways of measuring the quality of these estimators, using both classical statistical approaches and an expected-foregone-revenue approach.

Stochastic inflow modeling for hydropower scheduling problems

We introduce a new stochastic model for inflow time series that is designed with the requirements of hydropower scheduling problems in mind. The model is an “iterated function system’’: it models inflow as continuous, but the random innovation at each time step has a discrete distribution. With this inflow model, hydro-scheduling problems can be solved by the stochastic dual dynamic programming (SDDP) algorithm exactly as posed, without the additional sampling error introduced by sample average approximations. The model is fitted to univariate inflow time series by quantile regression. We consider various goodness-of-fit metrics for the new model and some alternatives to it, including performance in an actual hydro-scheduling problem. The numerical data used are for inflows to New Zealand hydropower reservoirs.