Implementation of different computational variations of biconjugate residual methods

AbstractIn this paper, we describe the derivation of the biconjugate residual (BCR) method from the general framework of the Block-CG algorithm; we then introduce different versions of BCR and test their numerical performance

Spatial Auction Markets with Unique Consumer Price

We consider a collection of auctions representing zonal electricity markets, which are joined by transmission lines in a spatial system. At each market, generating companies (traders) and customers (buyers) submit their fixed offer/bid prices together with maximal offer/bid volumes, respectively. In addition to the usual balance and capacity constraints, we consider also the additional requirement of utilizing the minimal unique purchase price for all the zones. As a result, we obtain spatial equilibrium type problems with special parameter for finding zonal prices and offer/bid volumes. We show that the streamlined formulation can be inconsistent under rather natural assumptions and propose a relaxed formulation. This problem admits suitable solution methods. We propose a parametric method combined with a bisection type procedure to solve this problem

Cournot equilibria in oligopolistic electricity markets

Electricity markets are undergoing a liberalization process aiming at introducing competition and enhancing efficiency. In liberalized markets, quantities and prices are determined by the interactions among the different players: power producers determine their production levels so as to maximize their own profits, while energy prices and demand levels to be satisfied are decided by an independent system operator (ISO). Deregulated electricity markets are very often oligopolistic, therefore the market equilibrium resulting from the interactions among power producers and ISO can be well represented by oligopolistic models. Thus, models based on game theory are used to describe the oligopolistic strategic interactions between the firms involved, representing the market as a non-cooperative game where players decide their strategy in order to maximize their profit. This paper presents a model that describes the strategic interactions of firms based on the assumption that the generation firms are Cournot oligopolists. A linear demand curve is assumed. Moreover, a new iterative algorithm is presented for determining the Cournot equilibrium and a case study is discussed

A two-stage stochastic optimization model for a gas sale retailer

The paper deals with a new stochastic optimization model, named OMoGaS-SV (Optimization Modelling for Gas Seller-Stochastic Version), to assist companies dealing with gas retail commercialization. Stochasticity is due to the dependence of consumptions on temperature uncertainty. Due to nonlinearities present in the objective function, the model can be classified as an NLP mixed integer model, with the profit function depending on the number of contracts with the final consumers, the typology of such consumers and the cost supported to meet the final demand. Constraints related to a maximum daily gas consumption, to yearly maximum and minimum consumption in order to avoid penalties and to consumption profiles are included. The results obtained by the stochastic version give clear indication of the amount of losses that may appear in the gas seller's budget and are compared with the results obtained by the deterministic version (see Allevi et al. [2])

Truncated Newton methods based on the ABS class

ABS - Abaffy-Broyden-SpedicatoAvailable from British Library Document Supply Centre- DSC:DX97191 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo