Luís A. C. Roque

A hybrid biased random key genetic algorithm approach for the unit commitment problem

This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. In the UC problem, the goal is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, the solution must satisfy a set of technological and operational constraints. The algorithm developed is a hybrid biased random key genetic algorithm (HBRKGA). It uses random keys to encode the solutions and introduces bias both in the parent selection procedure and in the crossover strategy. To intensify the search close to good solutions, the GA is hybridized with local search. Tests have been performed on benchmark large-scale power systems. The computational results demonstrate that the HBRKGA is effective and efficient. In addition, it is also shown that it improves the solutions obtained by current state-of-the-art methodologies.

A biased random key genetic algorithm approach for unit commitment problem

A Biased Random Key Genetic Algorithm (BRKGA) is proposed to find solutions for the unit commitment problem. In this problem, one wishes to schedule energy production on a given set of thermal generation units in order to meet energy demands at minimum cost, while satisfying a set of technological and spinning reserve constraints. In the BRKGA, solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as in the crossover strategy. Tests have been performed on benchmark large-scale power systems of up to 100 units for a 24 hours period. The results obtained have shown the proposed methodology to be an effective and efficient tool for finding solutions to large-scale unit commitment problems. Furthermore, from the comparisons made it can be concluded that the results produced improve upon some of the best known solutions.

An optimal control approach to the Unit Commitment problem

The Unit Commitment (UC) problem is a wellknown combinatorial optimization problem arising in operations planning of power systems. It is typically formulated as nonlinear mixed-integer programming problem and has been solved in the literature by a huge variety of optimization methods, ranging from exact methods (such as dynamic programming, branch-and-bound) to heuristic methods (genetic algorithms, simulated annealing, particle swarm). Here, we start by formulating the UC problem as a mixed-integer optimal control problem, with both binary-valued control variables and real-valued control variables. Then, we use a variable time transformation method to convert the problem into an optimal control problem with only real-valued controls. Finally, this problem is transcribed into a finite-dimensional nonlinear programming problem to be solved using an optimization solver.

Optimal Control Formulations for the Unit Commitment Problem

The Unit Commitment (UC) problem is a well-known combinatorial optimization problem arising in operations planning of power systems. It involves deciding both the scheduling of power units – when each unit should be turned on or off–, and the economic dispatch problem – how much power each of the on units should produce –, in order to meet power demand at minimum cost, while satisfying a set of operational and technological constraints. This problem is typically formulated as nonlinear mixed-integer programming problem and has been solved in the literature by a huge variety of optimization methods, ranging from exact methods (such as dynamic programming, branch-and-bound) to heuristic methods (genetic algorithms, simulated annealing, particle swarm). Here, we discuss how the UC problem can be formulated with an optimal control model, describe previous discrete-time optimal control models, and propose a continuous-time optimal control model. The continuous-time optimal control formulation proposed has the advantage of involving only real-valued decision variables (controls) and enables extra degrees of freeDalila B.M.M. Fontes LIAAD INESC TEC and Faculdade de Economia, Universidade do Porto Rua Dr. Roberto Frias, 4200-464 Porto, Portugal. e-mail: fontes@fep.up.pt Fernando A.C.C. Fontes Instituto de Sistemas e Robótica do Porto and Faculdade de Engenharia, Universidade do Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal. e-mail: faf@fe.up.pt Luı́s A.C. Roque Departamento de Matemática, Instituto Superior de Engenharia do Porto, R. Dr. Ant. Bernardino de Almeida, 431, 4200-072 Porto, Portugal. e-mail: lar@isep.ipp.pt ∗ Research partially supported by FCT POCI and FEDER through Projects PTDC/EGEGES/099741/2008, PTDC/EEA-CRO/116014/2009, and Marie Curie FP7-ITN-264735-SADCO.

New Formulations for the Unit Commitment Problem - Optimal Control and Switching-Time Parameterization Approaches.

The Unit Commitment Problem (UCP) is a well-known combinatorial optimization problem in power systems. The main goal in the UCP is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, a set of technological and operational constraints must be satisfied. A large variety of optimization methods addressing the UCP is available in the literature. This panoply of methods includes exact methods (such as dynamic programming, branch-and-bound) and heuristic methods (tabu search, simulated annealing, particle swarm, genetic algorithms). This paper proposes two non-traditional formulations. First, the UCP is formulated as a mixed-integer optimal control problem with both binary-valued control variables and real-valued control variables. Then, the problem is formulated as a switching time dynamic optimization problem involving only real-valued controls.