scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Implementation of a Lagrangian relaxation based unit commitment problem

TL;DR: The Lagrangian relaxation methodology has been used for solving the unit commitment problem as discussed by the authors, which is a class of complex combinatorial optimization problems in the power system, where the objective is to obtain an overall least-cost solution for operating the system over the scheduling horizon.
Abstract: The unit commitment problem in a power system involves determining a start-up and shut-down schedule of units to be used to meet the forecasted demand, over a future short term (24-168 hour) period. In solving the unit commitment problem, generally two basic decisions are involved. The "unit commitment" decision involves determining which generating units are to be running during each hour of the planning horizon, considering system capacity requirements including reserve, and the constraints on the start up and shut down of units. The related "economic dispatch" decision involves the allocation of system demand and spinning reserve capacity among the operating units during each specific hour of operation. As these two decisions are interrelated, the unit commitment problem generally embraces both these decisions, and the objective is to obtain an overall least cost solution for operating the power system over the scheduling horizon. The unit commitment problem belongs to the class of complex combinatorial optimization problems. During the past decade a new approach named "Lagrangian Relaxation" has been evolving for generating efficient solutions for this class of problems. It derives its name from the well-known mathematical technique of using Lagrange multipliers for solving constrained optimization problems, but is really a decomposition technique for the solution of large scale mathematical programming problems. The Lagrangian relaxation methodology generates easy subproblems for deciding commitment and generation schedules for single units over the planning horizon, independent of the commitment of other units.
Citations
More filters
Journal ArticleDOI
TL;DR: This paper presents a detailed overview of the basic concepts of PSO and its variants, and provides a comprehensive survey on the power system applications that have benefited from the powerful nature ofPSO as an optimization technique.
Abstract: Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed.

2,147 citations


Cites methods from "Implementation of a Lagrangian rela..."

  • ...…of optimization technique has been extensively used by researchers for solving problems, such as power system voltage security [28], [29], optimal power flow [30]–[33], power system operation and planning [34]–[38], dynamic security [39], [40], power quality [41], unit commitment [42], reactive…...

    [...]

Journal ArticleDOI
TL;DR: This paper presents a genetic algorithm (GA) solution to the unit commitment problem using the varying quality function technique and adding problem specific operators, satisfactory solutions to theunit commitment problem were obtained.
Abstract: This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported.

1,119 citations

Journal ArticleDOI
TL;DR: In this article, a bibliographical survey, mathematical formulations, and general backgrounds of research and developments in the field of modern unit commitment (UC) problem for past 35 years based on more than 150 published articles.
Abstract: With the fast-paced changing technologies in the power industry, new power references addressing new technologies are coming to the market. So there is an urgent need to keep track of international experiences and activities taking place in the field of modern unit-commitment (UC) problem. This paper gives a bibliographical survey, mathematical formulations, and general backgrounds of research and developments in the field of UC problem for past 35 years based on more than 150 published articles. The collected literature has been divided into many sections, so that new researchers do not face any difficulty in carrying out research in the area of next-generation UC problem under both the regulated and deregulated power industry.

898 citations


Cites background from "Implementation of a Lagrangian rela..."

  • ...Formally, we can write the UC problem as follows [30], [86], [126], [128]:...

    [...]

Journal ArticleDOI
TL;DR: The practical implementation of this procedure yielded satisfactory results when the EP-based algorithm was tested on a reported UC problem previously addressed by some existing techniques such as Lagrange relaxation (LR), dynamic programming (DP), and genetic algorithms (GAs).
Abstract: The work was conducted with the aim of finding a general method for solving the unit commitment (UC) problem. The proposed algorithm employs the evolutionary programming (EP) technique in which populations of contending solutions are evolved through random changes, competition, and selection. In the subject algorithm an overall UC schedule is coded as a string of symbols and viewed as a candidate for reproduction. Initial populations of such candidates are randomly produced to form the basis of subsequent generations. The practical implementation of this procedure yielded satisfactory results when the EP-based algorithm was tested on a reported UC problem previously addressed by some existing techniques such as Lagrange relaxation (LR), dynamic programming (DP), and genetic algorithms (GAs). Numerical results for systems of up to 100 units are given and commented on.

523 citations

Journal ArticleDOI
TL;DR: Several optimization techniques have been applied to the solution of the thermal unit commitment problem as discussed by the authors, ranging from heuristics such as complete enumeration to the more sophisticated ones such as augmented LaGrangian.
Abstract: Several optimization techniques have been applied to the solution of the thermal unit commitment problem. They range from heuristics such as complete enumeration to the more sophisticated ones such as Augmented LaGrangian. The heuristics have even reappeared as expert systems. The problem to solve is the optimal scheduling of generating units over a short-term horizon, typically 168 hours. This paper is an overview of the literature in the unit commitment field over the past twenty five years. >

518 citations

References
More filters
Journal ArticleDOI
TL;DR: This paper is a review of Lagrangian relaxation based on what has been learned in the last decade and has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering.
Abstract: (This article originally appeared in Management Science, January 1981, Volume 27, Number 1, pp. 1-18, published by The Institute of Management Sciences.) One of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints. Dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal value of the original problem. The Lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm. This approach has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering. This paper is a review of Lagrangian relaxation based on what has been learned in the last decade.

2,318 citations

Journal ArticleDOI
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
Abstract: The "relaxation" procedure introduced by Held and Karp for approximately solving a large linear programming problem related to the traveling-salesman problem is refined and studied experimentally on several classes of specially structured large-scale linear programming problems, and results on the use of the procedure for obtaining exact solutions are given It is concluded that the method shows promise for large-scale linear programming

1,339 citations

Journal ArticleDOI
TL;DR: This approach has obtained and verified optimal solutions to all the Kuehn-Hamburger location problems in well under 0.1 seconds each on an IBM 360/91 computer, with no branching required.
Abstract: We develop and test a method for the uncapacitated facility location problem that is based on a linear programming dual formation. A simple ascent and adjustment procedure frequently produces optimal dual solutions, which in turn often correspond directly to optimal integer primal solutions. If not, a branch-and-bound procedure completes the solution process. This approach has obtained and verified optimal solutions to all the Kuehn-Hamburger location problems in well under 0.1 seconds each on an IBM 360/91 computer, with no branching required. Computational tests on problems with as many as 100 potential facility locations provide evidence that this approach is superior to several other methods.

914 citations

Journal ArticleDOI
TL;DR: This tutorial provides a practical guide to the use of Lagrangian relaxation and an on-line computerized routing and scheduling optimizer.
Abstract: Lagrangian relaxation is a tool that is increasingly being used in large-scale mathematical programming applications, such as last year's CPMS/TIMS Management Achievement Award winner (Bell, W. J., L. M. Dalberto, M. L. Fisher, A. J. Greenfield, R. Jaikumar, P. Kedia, R. G. Mack, P. J. Prutzman. 1983. Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces 13(6, December) 4–23.). In this tutorial, Marshall Fisher provides a practical guide to the use of the approach with many examples and illustrations.

642 citations

Journal ArticleDOI
TL;DR: A mathematically based, systematic and generally applicable procedure to search for a reserve-feasible dual solution for power system generator unit commitment, giving reliable performance and low execution times.
Abstract: A Lagrangian relaxation algorithm for power system generator unit commitment is proposed. The algorithm proceeds in three phases. In the first phase, the Lagrangian dual of the unit commitment is maximized by standard subgradient techniques. The second phase finds a reserve-feasible dual solution, followed by a third phase of economic dispatch. A mathematically based, systematic and generally applicable procedure to search for a reserve-feasible dual solution is presented. The algorithm has been tested on systems of up to 100 units to be scheduled over 168 hours, giving reliable performance and low execution times. Both spinning and time-limited reserve constraints are treated. >

474 citations