Mette Bjørndal

Equilibrium prices supported by dual price functions in markets with non-convexities

The issue of finding market clearing prices in markets with non-convexities has had a renewed interest due to the deregulation of the electricity sector. In the day-ahead electricity market, equilibrium prices are calculated based on bids from generators and consumers. In most of the existing markets, several generation technologies are present, some of which have considerable non-convexities, such as capacity limitations and large start-up costs. In this paper we present equilibrium prices composed of a commodity price and an uplift charge. The prices are based on the generation of a separating valid inequality that supports the optimal resource allocation. In the case when the sub-problem generated as the integer variables are held fixed to their optimal values possess the integrality property, the generated prices are also supported by non-linear price functions that are the basis for integer programming duality.

Productivity Change and Innovation in Norwegian Electricity Distribution Companies

Regulators of electricity distribution networks have typically applied Data Envelopment Analysis (DEA) to cross-section data for benchmarking purposes. However, the use of panel data to analyse the impact of regulatory policies on productivity change over time is less frequent. The main purpose of this paper is to construct a Malmquist productivity index to examine the recent productivity change experienced by Norwegian distribution companies between 2004 and 2007. The Malmquist index is decomposed in order to explore the sources of productivity change, and to identify the innovator companies that pushed the frontier forward each year. The input and output variables considered are those used by the Norwegian regulator. In order to reflect appropriately the exogenous conditions where the companies operate, the efficiency model used in this paper incorporates geography variables as outputs of the DEA model. Unlike the model used by the regulator, we included virtual weight restrictions in the DEA formulation to correct the biases in the DEA results that may be associated to a judicious choice of weights by some of the companies.

The Deregulated Electricity Market Viewed as a Bilevel Programming Problem

In this paper, we present a bilevel programming formulation of a deregulated electricity market. By examining the electricity market in this format, we achieve two things. First, the relation of the deregulated electricity market to general economic models that can be formulated as bilevel programming problems (e.g. Stackelberg leader-follower games and principal-agency models) becomes clear. Secondly, it provides an explanation of the reason why the so-called “folk theorems” can be proven to be false for electricity networks. The interpretation of the deregulated electricity market as a bilevel program also indicates the magnitude of the error that can be made if the electricity market model studied does not take into account the physical constraints of the electric grid, or oversimplifies the electricity network to a radial network.

Congestion management in the Nordic power market - counter purchases and zonal pricing

In this paper, we investigate methods for managing congestion on the grid in the Nordic power market. Specifically, we have considered the differences between using counter purchases as opposed to pricing out the transmission constraints of the grid. We show that the specific method used for congestion management greatly affects prices and therefore the surplus of the various agents, including the system operator. This means that the market agents may have preferences for one method, and take actions in order to influence which method is to be used. Based on this, we have studied the incentives and possibilities of “moving” capacity constraints, and the effect this has on system performance. We have also looked into the differences between various pricing schemes, i.e. optimal nodal prices versus optimal zonal prices. The effects that are demonstrated by the examples in this paper are especially relevant when designing coordination mechanisms and regulation for integrated markets, like the (emerging) European electricity market.

Some thoughts on combinatorial optimisation

Abstract A group of young researchers from the ESI X summer school, HEC, Jouy-en-Josas 1994, give their personal views on the current status of, and prospects for, Combinatorial Optimisation. Several issues are considered and discussed with emphasis on a selected number of techniques: heuristics and polyhedral approaches, and problems: knapsack, quadratic 0–1 programming, machine scheduling, routing and network design.

Benchmarking in Regulation of Electricity Networks in Norway: An Overview

In this paper, we give an overview of the Norwegian regulation of electricity networks after the Energy Act of 1990 and the deregulation of the electricity markets in 1991. We concentrate on the regulatory oversight of distribution network companies and regional transmission. Our main focus is on the benchmarking models, including the application of their results, in the three periods of incentive regulation that we have seen so far, after its introduction in 1997. We examine the various data envelopment analysis (DEA) models that have been used, and we describe specific issues driving their development and how the results have been used.

Congestion management by dispatch or re-dispatch: Flexibility costs and market power effects

Several European electricity spot markets use simplified methods such as uniform or zonal pricing. These methods only partly address congestion. Re-dispatch is then necessary to achieve a feasible flow. In the assessment of congestion methods we address congestion methods in both spot and re-dispatch markets. The paper first shows that simplified methods (e.g. uniform pricing) combined with re-dispatch, in theory can achieve the maximum optimal surplus of the nodal pricing method. This however only occurs under the assumptions of full participation in re-dispatch and no extra costs of readjustment. We show that violations of these assumptions, i.e. limited participation and extra costs of readjustment can make the spot and re-dispatch model of handling congestion inefficient compared to nodal pricing. Further, we show that when a strategic player operates in the spot and re-dispatch market model, the consequences of market power potentially may be more severe and difficult to detect.

Nodal pricing in a coupled electricity market

This paper investigates a pricing model for an electricity market with a hybrid congestion management method, i.e. part of the system applies a nodal pricing scheme and the rest applies a zonal pricing scheme. The model clears the zonal and nodal pricing areas simultaneously. The nodal pricing area is affected by the changes in the zonal pricing area since it is directly connected to the zonal pricing area by commercial trading. The model is tested on a 13-node power system. Within the area that is applying nodal pricing, prices and surpluses given by the hybrid pricing model match well with those given by the full nodal pricing model. Part of the network is better utilized compared to the solutions given by the full zonal pricing model. However, the prices given by the hybrid system may send wrong economic signals which triggers unnecessary generation from existing capacities, exacerbates grid congestion, and induces higher re-dispatching costs.

An Analysis of a Combinatorial Auction

Our objective is to find prices on individual items in a combinatorial auction that support the optimal allocation of bundles of items, i.e. the solution to the winner determination problem of the combinatorial auction. The item-prices should price the winning bundles according to the corresponding winning bids, whereas the bundles that do not belong to the winning set should have strictly positive reduced cost. I.e. the bid on a non-winning bundle is strictly less than the sum of prices of the individual items that belong to the bundle, thus providing information to the bidders why they are not in the winning set. Since the winner determination problem is an integer program, in general we cannot find a linear price-structure with these characteristics. However, in this article we make use of sensitivity analysis and duality in linear programming to obtain this kind of price-information. Finally, it is indicated how such prices can be used to enhance economic efficiency in an iterative market design. Throughout, the ideas are illustrated by means of numerical examples.

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.