Download or read book Strong Stationary Solutions to Equilibrium Problems with Equilibrium Constraints with Applications to an Electricity Spot Market Model written by René Henrion and published by . This book was released on 2009 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literaturverz. S. 26 - 27.

Download or read book On M stationary Points for a Stochastic Equilibrium Problem Under Equilibrium Constraints in Electricity Spot Market Modeling written by René Henrion and published by . This book was released on 2007 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Non Smooth and Complementarity Based Distributed Parameter Systems written by Michael Hintermüller and published by Springer Nature. This book was released on 2022-02-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

Download or read book Equilibrium Problems with Equilibrium Constraints and Their Application to Electricity Markets written by Andreas Ehrenmann and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Variational Analysis and Generalized Differentiation in Optimization and Control written by Regina S. Burachik and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some 20 papers describing recent developments in advanced variational analysis, optimization, and control systems, especially those based on modern variational techniques and tools of generalized differentiation.

Download or read book Cournot Equilibrium in Two settlement Electricity Markets written by Jian Yao and published by . This book was released on 2006 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equilibrium Problems with Equilibrium Constraints written by Che-Lin Su and published by . This book was released on 2005 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Explicit stationarity conditions and solution characterization for equilibrium problems with equilibrium constraints written by and published by . This book was released on 2010 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nash Equilibrium Problems in Power Markets and Product Design Analysis and Algorithms written by Aswin Kannan and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this research is on the analysis and computation of equilibria in noncooperative Cournot and Bertrand games. The application of focus for Cournot competition is power markets while that for Bertrand competition is product design. We consider Cournot-based models for strategic behavior in power markets while Bertrandbased models are employed for analyzing the behavior of price-based competition in product design. This thesis is partitioned into three parts. Of these, the rst two parts focus on power market applications while the third part focuses on product design. Motivated by the risk of capacity shortfall faced by market participants with uncertain generation assets, the rst part considers a game where agents are assumed to be risk-averse optimizers, using a conditional value-at-risk (CVaR) measure. The resulting game-theoretic problem is a two-period risk-based stochastic Nash game with shared strategy sets. In general, this stochastic game has nonsmooth objectives and standard existence and uniqueness results cannot be leveraged for this class of games, given the lack of compactness of strategy sets and the absence of strong monotonicity in the gradient map of the objectives. However, when the risk-measure is independent of competitive interactions, a subset of equilibria to the risk-averse game are shown to be characterized by a solvable monotone single-valued variational inequality. If the risk-measures are generalized to allow for strategic interactions, then the characterization is through a multi-valued variational inequality. Both this object and its single-valued counterpart, arising from the smoothed game, are shown to admit solutions. The equilibrium conditions of the game grow linearly in size with the the sample-space, network size and the number of participating rms. Consequently, direct schemes are inadvisable for most practical problems and instead, we present a distributed regularized primaldual and dual projection scheme where both primal and dual iterates are computed separately. Rate of convergence estimates are provided and error bounds are developed for inexact extensions of the dual scheme. Unlike projection schemes for deterministic problems, here the projection step requires the solution of a possibly massive stochastic program. By utilizing cutting plane methods, we ensure that the complexity of the projection scheme scales slowly with the size of the sample-space. Insights regarding market design and operation are obtained after testing the model on a 53-node electricity network. The second part extends this model by considering the grid operator to be a pro t maximizer. However the effect of risk is neglected in this model. The resulting problem is a quasi variational inequality. An analysis of the equivalent complementarity problem (CP) allows us to claim that the game does admit an equilibrium. By observing that the CP is monotone, we are in a position to employ a class of iterative regularization techniques namely the iterative Tikhonov and the iterative proximal algorithms. The algorithms are seen to scale well with the size of the problem. The model is employed for examining strategic behavior on a twelve node network and several economic insights are drawn. The third part of this thesis deals with Bertrand competition in a product design regime. With due consideration to the attribute dimension in addition to price competition, more specifically for design and consumer service industries, a game theoretic model is formulated. The logit model, in lieu of some of its tractable properties, is deployed to capture consumer preferences and thereby the demand. Subsequently the variational formulations corresponding to the game are analyzed for existence of solutions. The lack of convexity of objectives, analytical intractability of the variational formulations corresponding to the game state some drawbacks of the logit model. Several projection and interior point schemes are deployed for solving these classes of problems. Numerical results for smaller instances of these games are illustrated by means of a painkiller example. Suggestions on alternate revenue maximization models are presented.

Download or read book Competition and Equilibria in Electricity Markets Based on Two settlement System written by David Watts and published by . This book was released on 2007 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Modelling of Electricity and Related Markets written by Fred Espen Benth and published by World Scientific. This book was released on 2008 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives. This book provides a concise and rigorous treatment on the stochastic modeling of energy markets. OrnsteinOCoUhlenbeck processes are described as the basic modeling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes. Temperature futures are studied based on a continuous higher-order autoregressive model for the temperature dynamics. The theory presented here pays special attention to the seasonality of volatility and the Samuelson effect. Empirical studies using data from electricity, temperature and gas markets are given to link theory to practice. Sample Chapter(s). A Survey of Electricity and Related Markets (331 KB). Contents: A Survey of Electricity and Related Markets; Stochastic Analysis for Independent Increment Processes; Stochastic Models for the Energy Spot Price Dynamics; Pricing of Forwards and Swaps Based on the Spot Price; Applications to the Gas Markets; Modeling Forwards and Swaps Using the HeathOCoJarrowOCoMorton Approach; Constructing Smooth Forward Curves in Electricity Markets; Modeling of the Electricity Futures Market; Pricing and Hedging of Energy Options; Analysis of Temperature Derivatives. Readership: Researchers in energy and commodity markets, and mathematical finance.

Download or read book Incorporating Fuel Constraints and Electricity Spot Prices Into the Stochastic Unit Commitment Problem written by Samer Takriti and published by . This book was released on 1997 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The electric power industry is going through deregulation. As a result, the load on the generating units of a utility is becoming increasingly unpredictable. Furthermore, electric utilities may need to buy power or sell their production to a power pool which serves as a spot market for electricity. These trading activities expose utilities to volatile electricity prices. In this paper, we present a stochastic model for the unit commitment that incorporates power trading into the picture. Our model also accounts for fuel constraints and prices which may vary with electricity prices and demand. The resulting model is a mixed-integer program which is solved using Lagrangian relaxation and Bender's decomposition. Using this solution approach, we solve problems with 729 demand scenarios on a single processor to within O.1% of the optimal solution in less than 10 minutes. Our numerical results indicate that significant savings can be achieved when the spot market is entered into the problem and when a stochastic policy is adopted instead of a deterministic one."

Download or read book Optimization and Equilibrium Methods in Power Systems written by and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Efficient operation and planning of electric power systems promise huge gains to society, from reduction of global poverty to avoidance of drastic climate change. There is a great need for mathematical and economic modeling to support these efficiency efforts. This thesis explores optimization methods to directly improve planning and operation and equilibrium methods to understand how markets composed of multiple economic agents carry out these optimal plans or in some cases thwart them. The challenges faced by this thesis are rooted not only in economic behavior and engineered systems but also in mathematical complexity. We characterize the mode of divergence of agent-decomposable iterative algorithms for equilibrium problems. These problems pose a challenge for agent-decomposable algorithms because the applications where equilibrium seems to be most necessary for a faithful model have strong interactions between agents. We introduce an equilibrium model for understanding the effect of risk aversion in investment in power grid components. We develop a novel global optimization technique for a nonconvex problem arising from coal mine quality planning. Our technique relies on isolating the nonconvexity to a low dimensional structure, which is then approximated by a discrete grid. The low dimensionality keeps the computational cost manageable. We model the effect of unit commitment on the behavior of strategic power suppliers under various market rules by computing discrete approximations of mixed Nash equilibria in continuous spaces. We are able consider rules such as a single price, a price with an uplift, and pay-as-bid. We also document our contributions to collaborative work on semidefinite programming relaxations of nonconvex power flow problems and on the social benefit of expanded bidding structures in wholesale power markets.

Download or read book Supply Function Equilibrium in Electricity Markets written by Keith Ruddell and published by . This book was released on 2017 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supply function equilibrium (SFE) models strategic offering in oligopolistic wholesale electricity auctions. In the supply function game, the strategies are curves giving the output levels offered at different prices. Generators submit their offer curves to the system operator, knowing the demand level only in distribution. A Nash equilibrium in these curves is found when each generator's offer is optimal, given the other offers, the demand distribution, and possible constraints and side payments. The theory for pool-market SFE with uniform pricing is well developed. This thesis explores several variations on SFE models. SFE models that include side payments arising from contracting arrangements or vertical integration between generators and retailers are developed. We find that forward sales through contracts for differences, options, and fixed price variable volume contracts all lead to lower wholesale prices, though each type of contract has a distinct effect on the shape of the price distribution. We consider non-uniform pricing rules, with an application to transmission pricing. The analysis is also extended to generators who act as price takers. The equilibrium conditions for SFE take the form of differential equations. Under appropriate assumptions on cost and demand functions, we obtain a planar autonomous system of ordinary differential equations for the SFE over a single lossless constrained transmission line. Computational methods are developed to handle monotonicity constraints on the supply functions, and then applied to topical electricity market policy questions on the competitive effects of: the rise of wind generation, futures and options trading, financial transmission rights, and asset swaps - real and virtual. Finally, a supply function equilibrium model is constructed for an auction in which multiple products are settled simultaneously, in which bids and offers are allowed to express cross-elasticities in demand and cost. With these new computational methods, it becomes possible to more accurately model the wholesale electricity market, and derive new insights into questions of market power and market design.

Download or read book Decomposition of Variational Inequalities with Applications to Nash Cournot Models in Time of Use Electricity Markets written by Emre Celebi and published by . This book was released on 2011 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes equilibrium models to link the wholesale and retail electricity markets which allow for reconciliation of the differing time scales of responses of producers (e.g., hourly) and consumers (e.g., monthly) to changing prices. Electricity market equilibrium models with time of use (TOU) pricing scheme are formulated as large-scale variational inequality (VI) problems, a unified and concise approach for modeling the equilibrium. The demand response is dynamic in these models through a dependence on the lagged demand. Different market structures are examined within this context. With an illustrative example, the welfare gains/losses are analyzed after an implementation of TOU pricing scheme over the single pricing scheme. An approximation of the welfare change for this analysis is also presented. Moreover, break-up of a large supplier into smaller parts is investigated. For the illustrative examples presented in the dissertation, overall welfare gains for consumers and lower prices closer to the levels of perfect competition can be realized when the retail pricing scheme is changed from single pricing to TOU pricing. These models can be useful policy tools for regulatory bodies i) to forecast future retail prices (TOU or single prices), ii) to examine the market power exerted by suppliers and iii) to measure welfare gains/losses with different retail pricing schemes (e.g., single versus TOU pricing). With the inclusion of linearized DC network constraints into these models, the problem size grows considerably. Dantzig-Wolfe (DW) decomposition algorithm for VI problems is used to alleviate the computational burden and it also facilitates model management and maintenance. Modification of the DW decomposition algorithm and approximation of the DW master problem significantly improve the computational effort required to find the equilibrium. These algorithms are applied to a two-region energy model for Canada and a realistic Ontario electricity test system. In addition to empirical analysis, theoretical results for the convergence properties of the master problem approximation are presented for DW decomposition of VI problems.

Download or read book Numerical Solutions of Electricity Market Equilibrium and Collusion Models with AMPL and MATLAB written by Grant Francis Roch and published by . This book was released on 2004 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: