Mario Veiga Pereira

A New Benders Decomposition Approach to Solve Power Transmission Network Design Problems

In this paper we describe a new Benders decomposition approach to solve power transmission network expansion planning problems. This new approach is characterized by using a linear (0-1) disjuntictive model that ensures the optimality of the solution found and by using additional constraints, iteratively evaluated, besides the traditional Benders cuts. The results obtained, considering a real world power transmission network expansion planning study with the southeastem Brazilian system, show the efficiency of this approach.

A Mixed Integer Disjunctive Model for Transmission Network Expansion

The classical nonlinear mixed integer formulation of the transmission network expansion problem cannot guarantee finding the optimal solution due to its nonconvex nature. We propose an alternative mixed integer linear disjunctive formulation, which has better conditioning properties than the standard disjunctive model. The mixed integer program is solved by a commercial branch and bound code, where an upper bound provided by a heuristic solution is used to reduce the tree search. The heuristic solution is obtained using a GRASP metaheuristic, capable of finding sub-optimal solutions with an affordable computing effort. Combining the upper bound given by the heuristic and the mixed integer disjunctive model, optimality can be proven for several hard problem instances.

Application Of Sensitivity Analysis Of Load Supplying Capability To Interactive Transmission Expansion Planning

This paper illustrates the application of sensitivity methods as a tool for long-term transmission expansion planning. Possible investments are ranked in accordance with their effectiveness in increasing the system load supplying capability or reducing the system load curtailment. The calculation of these indices is performed as a special case of the optimal dispatch problem, for which very efficient solution algorithms are available. A case study with the system of Southern Brazil is used to evaluate the performance of the ranking algorithms.

A Decomposition Approach To Automated Generation/Transmission Expansion Planning

This paper describes a model for automated generation/transmission expansion to be used in longterm system planning studies. The network is represented either by a transportation model or by a linearized power flow model. The solution technique is based on Benders decomposition, maximum flow algorithms and linear programming/optimal dispatch models. Case studies with the system of Southern Brazil are presented and discussed.

Strategic bidding under uncertainty: a binary expansion approach

This work presents a binary expansion (BE) solution approach to the problem of strategic bidding under uncertainty in short-term electricity markets. The BE scheme is used to transform the products of variables in the nonlinear bidding problem into a mixed integer linear programming formulation, which can be solved by commercially available computational systems. The BE scheme is applicable to pure price, pure quantity, or joint price/quantity bidding models. It is also possible to represent transmission networks, uncertainties (scenarios for price, quantity, plant availability, and load), financial instruments, capacity reinforcement decisions, and unit commitment. The application of the methodology is illustrated in case studies, with configurations derived from the 80-GW Brazilian system.

Combining analytical models and Monte-Carlo techniques in probabilistic power system analysis

The authors describe a general framework for combining analytical models and Monte Carlo simulation. The basic idea is to use a simpler analytical model as an approximation to a more detailed model in a Monte Carlo simulation scheme. The simulation then deals with the residual, i.e. the difference between the result of the detailed model and the approximation. The component of probabilistic indices which can be explained by the analytical model is factored out of the Monte Carlo sampling scheme, which then handles only the unexplained residuals. The proposed scheme is flexible and easy to implement, as no modification of existing analytical models is required. The approach is illustrated in case studies with utility-derived systems in several application areas: composite reliability evaluation, multi-area production costing, chronological production costing with ramping constraints, and operation of a multireservoir hydroelectric system. >

Nash equilibrium in strategic bidding: a binary expansion approach

This paper presents a mixed integer linear programming solution approach for the equilibrium problem with equilibrium constraints (EPEC) problem of finding the Nash equilibrium (NE) in strategic bidding in short-term electricity markets. A binary expansion (BE) scheme is used to transform the nonlinear, nonconvex, NE problem into a mixed integer linear problem (MILP), which can be solved by commercially available computational systems. The BE scheme can be applicable to Cournot, Bertrand, or joint price/quantity bidding models. The approach is illustrated in case studies with configurations derived from the 95-GW Brazilian system, including unit-commitment decisions to the price-maker agents.

Auctions of contracts and energy call options to ensure supply adequacy in the second stage of the Brazilian power sector reform

The reform process in the electricity sector of any country has as main objective the design of a power market capable to induce a reliable and efficient energy supply, translated into adequate tariffs. Brazil started its reform process in 1996, inspired by similar schemes in the electricity sector of more developed countries. However, the existence of particularities in the countrys hydroelectric energy market, such as weak spot price signals for system expansion and difficulties to determine benchmark prices, avoided a smooth transition to a fully deregulated market. In 2004, a revisited power sector model was launched, aiming at alleviating the difficulties of the first model. The core of the new proposals lies on the use of contract obligation and energy supply auctions as the backbone for the efficient contracting and supply adequacy. Supply auctions were held in 2004-2005, with a volume of about 20,000 average MW contracted involving about 60 billion USD in financial transactions. This work discusses the implementation of auctions of energy contracts and call options in Brazil as part of the mechanisms to ensure supply adequacy adopted in the second stage of its power sector reform

Stochastic Hydro-Thermal Scheduling Under

Despite the uncertainty surrounding the design of a mechanism which is ultimately accepted by nations worldwide, the necessity to implement regulations to curb emissions of greenhouse gases on a global scale is consensual. The electricity sector plays a fundamental role in this puzzle and countries may soon have to revise their operating policy directives in order to make them compatible with additional constraints imposed by such regulations. We present a modeling approach for greenhouse gas emissions quotas which can be incorporated into a stochastic dual dynamic programming algorithm, commonly used to solve the hydro-thermal scheduling problem. Our approach is flexible and capable of accommodating a detailed representation of emissions and related constraints. A case study based on the Guatemalan power system exemplifies the potential effects of considering these restrictions.

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Renewable sources have recently emerged as a generation option for many countries in order to promote clean energy development. In the case of Brazil, small hydro plants and cogeneration from sugarcane waste (bagasse) have been attractive alternatives during the past years, with hundreds of MW installed since 2004. Despite their advantages, both alternatives are hindered by seasonal yet complementary availability. This forces producers to discount (or price) the risks faced when selling firm energy contracts and may ultimately lead to projects being commercially unattractive. We propose a stochastic optimization model that defines the optimal composition of a portfolio based on these two renewable sources in order to maximize the revenue of an energy trading company. At the same time, this model mitigates hydrological and fuel unavailability risks, thus allowing the participation of both sources in the forward market environment in a competitive manner. A case study is presented, based on data from the Brazilian system.