Luiz Augusto Barroso

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.

Bilevel optimization applied to strategic pricing in competitive electricity markets

Abstract In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures is illustrated in case studies with configurations derived from the Brazilian power 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

Optimal Bidding Strategies for Hydro-Electric Producers: A Literature Survey

In a competitive environment with bid-based markets, power generation companies desire to develop bidding strategies that maximize their revenue. In this paper we ask: What approaches and methodologies have been used to model the bidding problem for hydro-electric producers? We present the problems developments over time and, through reviewing different variants of the problem, progressively build to the case in which the agent is a price-maker hydro-electric producer. In each variant of the bidding problem, we examine how the approaches used to solve it may or may not be applicable to other variants. Last, for the price-maker hydro-electric producers bidding problem, we recognize the most recent developments and illuminate a path for future efforts.

Time-of-Use Tariff Design Under Uncertainty in Price-Elasticities of Electricity Demand: A Stochastic Optimization Approach

Time-of-use (ToU) electricity tariffs are currently employed or considered for implementation in many jurisdictions around the world. In ToU modalities, a set of different tariffs for different hours of the day and/or seasons of the year is defined at the beginning of a given horizon, and then kept constant until its end. While designing ToU tariffs, one of the most significant sources of uncertainty to be considered relates to price-elasticities of demand. We propose an approach for ToU tariff design based in quadratically constrained quadratic programming and stochastic optimization techniques, addressing these uncertainties and dealing with various aspects of tariff design from the point of view of the regulator/regulated utility.

Risk Constrained Portfolio Selection of Renewable Sources in Hydrothermal Electricity Markets

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.

Allocation of Firm-Energy Rights Among Hydro Plants: An Aumann–Shapley Approach

The firm energy of generation plants is a critical component in some electricity markets. It is usually calculated by the regulator and sets a cap to the amount a plant can trade in capacity markets (or auctions), in order to avoid free-riding behaviors. Firm energy is a systemic property and, in case of hydro plants, a synergy is observed whenever a cooperative operation occurs, i.e., the firm energy of a system is greater than the sum of the individual plants. This immediately raises the question of how to divide the systems firm energy among the individual hydro plants. The objective of this work is to investigate the application of different allocation methods of firm energy rights among hydro plants using a game-theoretic framework. It is shown that there is not an optimal and unique approach to make this allocation. The paper investigates the advantages and disadvantages of different methods, such as marginal allocation, average production during the critical period, incremental allocation, finally recommending the Aumann-Shapley as the allocation method. This method is tested for the Brazilian power system, which has around 100 hydro plants. The results obtained are compared with the current allocation adopted by the electricity regulatory agency of Brazil.

South American reform lessons - twenty years of restructuring and reform in Argentina, Brazil, and Chile

South America is facing important challenges in electricity supply to allow for future economic development. Current electricity market designs are being reviewed to avoid supply difficulties and couple the existing outlook of primary energy resources and the investment interest by the private sector. While Brazil and Chile progress into a second stage of reforms with public power purchase agreement (PPA) auctions in a private environment, Argentina makes a backward movement to significant state intervention, as in the times previous to reform. This paper discusses the approaches to be used by each country to ensure sufficient capacity and investment to reliably serve their growing economies.

Pricing Flexible Natural Gas Supply Contracts Under Uncertainty in Hydrothermal Markets

The worldwide development of the natural gas industry resulted in an integration process between electrical and gas sectors in several countries. In Brazil, this process has been taking place in a consistent manner, especially on account of the increase in gas consumption for industrial use and of the installation of thermoelectric plants. Due to the predominance of hydro plants in electric power generation, thermoelectric energy production is basically dependent on hydrology and, as a result, presents a wide annual variability. Consequently, the investment applied to gas production and transportation infrastructure may become under-utilized during a large part of the time; thus, it is important to find mechanisms apt to improve its utilization. In this respect, the present work investigates the creation of a flexible market for gas, where contracts for flexible gas supply would be offered to industrial users, who would receive the gas assigned to thermal power plants when the latter are not dispatched, and would resort to an alternate fuel when these plants are dispatched. The attractiveness of such a contract would depend, of course, on its price. The purpose of this work is to develop a stochastic model for pricing flexible gas supply contracts, taking into account the uncertainty associated to the supply - dependent on the dispatch of the thermal power plants, which have the priority of use of the gas - and the risk profile of potential consumers.