Marcia Fampa

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.

An efficient heuristic for the ring star problem

In this paper, we consider a combinatorial optimization problem that arises in the design of telecommunications network. It is known as the Ring Star Problem. In this problem the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a routing cost proportional to the length of the cycle, and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. We propose a new hybrid metaheuristic approach to solve the Ring Star Problem. In the hybrid metaheuristic, we use a General Variable Neighborhood Search (GVNS) to improve the quality of the solution obtained with a Greedy Randomized Adaptive Search Procedure (GRASP). A set of extensive computational experiments on instances from the classical TSP library and randomly generated are reported, comparing the GRASP/GVNS heuristic with other heuristic found in the literature. These results indicate that the proposed hybrid metaheuristic is highly efficient and superior to the other available method proposed for the Ring Star Problem.

Bid-Based Dispatch of Hydrothermal Systems in Competitive Markets

The objective of this work is to investigate possible hydro-scheduling inefficiencies under a bidding scheme. It will be shown that the market-based dispatch of hydro-plants, under a perfect competitive market, converges to its least-cost dispatch. Besides, it will be shown that the usual spot payment scheme does not provide the correct incentive for upstream reservoirs to regulate downstream production, thus causing an operating distortion. The implementation of a Wholesale Water Market is proposed for trading stored water and so to correct such distortion. Case studies will be presented, with data taken from the Brazilian System.

Market Power Issues in Bid-Based Hydrothermal Dispatch

The objective of this work is to investigate market power issues in bid-based hydrothermal scheduling. Initially, market power was simulated with a single stage Cournot–Nash equilibrium model. In this static model the equilibrium was calculated analytically. It was shown that the total production of N strategic agents is smaller than the least-cost solution by a factor of (N/(N+1)). Market power analysis for multiple stages was then carried through a stochastic dynamic programming scheme, where the decision in each stage and state is the Cournot–Nash equilibrium of a multi-agent game. Case studies with data taken from the Brazilian system are presented.

Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Prob- lem - the problem of choosing the s x s principal submatrix with maximal determinant from a given n x n positive definite matrix, subject to linear constraints. We implement a branch-and- bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. A parallel implementation of the algorithm exhibits approximately linear speed-up for up to 8 processors, and has successfully solved problem instances which were heretofore intractable.

Maximum-entropy remote sampling

Abstract We consider the “remote-sampling” problem of choosing a subset S, with |S|=s, from a set N of observable random variables, so as to obtain as much information as possible about a set T of target random variables which are not directly observable. Our criterion is that of minimizing the entropy of T conditioned on S. We confine our attention to the case in which the random variables have a joint Gaussian distribution. We demonstrate that the problem is NP-complete. We provide two methods for calculating lower bounds on the entropy: (i) a spectral method, and (ii) a continuous nonlinear relaxation. We employ these bounds in a branch-and-bound scheme to solve problem instances to optimality.

Continuous Relaxations for Constrained Maximum-Entropy Sampling

We consider a new nonlinear relaxation for the Constrained Maximum Entropy Sampling Problem — the problem of choosing the s × s principal submatrix with maximal determinant from a given n × n positive definite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation.

Using a Conic Formulation for Finding Steiner Minimal Trees

We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an ε-optimal solution for this latter problem using an interior-point algorithm.