Sergio Granville

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.

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.

Dynamic security constrained optimal power flow/VAr planning

Traditionally security constrained optimal power flow and VAr planning methods consider static security observing voltage profile and flow constraints under normal and post contingency conditions. Ideally, these formulations should be extended to consider dynamic security. This paper reports on a BC Hydro/CEPEL joint effort establishing a dynamic security constrained OPF/VAr planning tool which considers simultaneously static constraints as well as voltage stability constraints. This paper covers the details of formulation and implementation of the tool together with the test results on a large scale North American utility system and a reduced Brazilian 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.

The Stackelberg equilibrium applied to AC power systems-a noninterior point algorithm

The electric utility deregulation process and the introduction of competition among its participants introduced the notion of equilibria models adapted to the energy market. Among them, the Stackelberg equilibrium represents a monopolist approach, defined by a hierarchical structure, with a dominant firm acting in a privileged position and a group of subordinated ones acting as followers. Its application to AC power systems can be modeled as a bilevel mathematical problem, and represented by its Karush Kuhn Tucker (KKT) formulation. This paper presents a noninterior point algorithm to solve this Stackelberg equilibrium, considering the electrical power system as an interconnected network through its transmission system. Numerical examples with a 24 bus and the IEEE-118 bus systems illustrated the leader participant behavior and showed the market power exercised by them, which is increased in the presence of tighter transmission capacity constraints. The numerical examples also showed the robustness and efficiency of the proposed algorithm.

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.

Recent advances of sugarcane biomass cogeneration in Brazil

the integrated sugar/ethanol/electricity production has launched a new business model — the bioelectricity industry — with a potential to become a “mainstream” energy supply option in the near future in Brazil. Besides being clean, the bioelectricity plants have been winning several hundred MWs in long-term contracts auctioned by distribution companies under the Brazilian power sector framework. These contracts have been awarded on a competitive basis, without any subsidy policy. In addition, bioelectricity plants comply with the requirements of the CDM for selling emission reduction credits. The objective of this work is to discuss the bioelectricity achievements in Brazil.

Risk constrained contracting strategies of renewable portfolios

The search for clean energy development has motivated the expansion of renewable sources of generation around the world. In Brazil, Small Hydro Plants (SHP), Cogeneration from Sugarcane waste (Biomass) and Wind Power Plants (WPP) are proving themselves to be attractive alternatives over the last years. One important characteristic of each of these technologies is their seasonal availability, which result in financial risks that can make the energy contracting of each individual source too risky: producers are forced to price the market risks faced when selling firm energy contracts (i.e., the risks of purchasing in the spot market whenever their production is smaller than the contracted amount) and this may ultimately lead each of the projects to not being as commercially attractive by itself. On the other hand, in Brazil these sources have complementary energy production patterns, which immediately suggest a portfolio approach to devise energy contracting strategies for Electricity Trading Companies (ETC), which can “blend” these different (and complementary) production patterns to offer a flat and firm energy delivery. The objective of this work is to develop a mathematical model to explore synergies due to the seasonal complementarities of a Biomass, a SHP and a WPP. The proposed model aims at composing an optimal portfolio of these sources and jointly determines the risk-constrained optimal trading strategy for selling an energy contract in the Brazilian forward contract market. The CVaR approach is used to measure and control the market risk associated to the energy delivery. Case studies will be presented with realistic data from the Brazilian power system showing different strategies of commercialization by an ETC.

Bidding strategies in auctions for long-term electricity supply contracts for new capacity

The objective of this work is to discuss the modeling of auctions of long-term electricity supply contracts for new capacity in Brazil. The modeling of risks such as price-quantity (hydrological) risk, project completion risk, environmental constraints, climate change and regulatory risks are discussed. An analytical model will be developed to price these risks and case studies will be presented for real projects that have participated in the Brazilian contract auctions for new capacity. We also discuss selection of projects with different risks.