Golbon Zakeri

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.

Inexact Cuts in Benders Decomposition

Benders decomposition is a well-known technique for solving large linear programs with a special structure. In particular, it is a popular technique for solving multistage stochastic linear programming problems. Early termination in the subproblems generated during Benders decomposition (assuming dual feasibility) produces valid cuts that are inexact in the sense that they are not as constraining as cuts derived from an exact solution. We describe an inexact cut algorithm, prove its convergence under easily verifiable assumptions, and discuss a corresponding Dantzig--Wolfe decomposition algorithm. The paper is concluded with some computational results from applying the algorithm to a class of stochastic programming problems that arise in hydroelectric scheduling.

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.

A comparison of stochastic programming and bi-objective optimisation approaches to robust airline crew scheduling

A prominent problem in airline crew scheduling is the pairings or Tour-of-Duty planning problem. The objective is to determine a set of pairings (or Tours-of-Duty) for a crew group to minimise the planned cost of operating a schedule of flights. However, due to unforeseen events the performance in operation can differ considerably from planning, sometimes causing significant additional recovery costs. In recent years there has been a growing interest in robust crew scheduling. Here, the aim is to find solutions that are “cheap” in terms of planned cost as well as being robust, meaning that they are less likely to be disrupted in case of delays. Taking the stochastic nature of delays into account, Yen and Birge (Transp Sci 40:3–14, 2006) formulate the problem as a two-stage stochastic integer programme and develop an algorithm to solve this problem. Based on the contradictory nature of the goals, Ehrgott and Ryan (J Multi-Criteria Decis Anal 11:139–150, 2002) formulate a bi-objective set partitioning model and employ elastic constraint scalarisation to enable the solution by set partitioning algorithms commercially used in crew scheduling software. In this study, we compare the two solution approaches. We improve the algorithm of Yen and Birge (Transp Sci 40:3–14, 2006) and implement both methods with a commercial crew scheduling software. The results of both methods are compared with respect to characteristics of robust solutions, such as the number of aircraft changes for crew. We also conduct experiments to simulate the performance of the obtained solutions. All experiments are performed using actual schedule data from Air New Zealand.

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.

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.

Pricing Wind: A Revenue Adequate, Cost Recovering Uniform Price for Electricity Markets with Intermittent Generation

With greater penetration of renewable generation, the uncertainty faced in electricity markets has increased substantially. Conventionally, generators are assigned a pre-dispatch quantity in advance of real time, based on estimates of uncertain quantities. Expensive real time adjustments then need to be made to ensure demand is met, as uncertainty takes on a realization. We propose a new stochastic-programming market clearing mechanism to optimize pre-dispatch quantities, given the uncertainties’ probability distribution and the costs of real-time deviation. This model differs from similar mechanisms previously proposed in that pre-dispatch quantities are not subject to any network or other physical constraints; nor do they play a role in financial settlement. We establish revenue adequacy in each scenario (as opposed to “in expectation”), welfare enhancement and expected cost recovery (including deviation costs), for this market clearing mechanism. We also establish that this market clearing mechanism is social welfare optimizing.

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.

Optimization of Demand Response Through Peak Shaving

Abstract We consider a consumer of a resource, such as electricity, who must pay a per unit charge to procure the resource, as well as a peak demand charge. We will assume that this consumer has some ability to self-generate and present an efficient linear programming formulation for the demand response of such a consumer. We will establish a monotonicity result that indicates fuel supply of S , utilized for self-generation, may be spent in successive steps adding to S .

Integrating Consumption and Reserve Strategies for Large Consumers in Electricity Markets

In this paper we present the development of a simulation model for large consumers to optimise their consumption and reserve offers in a security constrained electricity market. We utilise the New Zealand grid, which has security constrained generation and transmission which can influence marginal nodal pricing. To illustrate this influence we use a series of small optimal power flow models as well as illustrating how these may influence a large integrated consumer (who offers interruptible load). Our simulation model has been successful at determining periods during which a large consumer may reduce their consumption (demand response) in order to reduce the energy price. We expect this approach to be extensible to other markets although we note that information surrounding the underlying market structure will heavily influence the viability