Branch-and-bound scheduling for thermal generating units

Abstract

Scheduling thermal generation units plays an important role in power system economic operations. Each day power generating units have to be selected to realize a reliable production of electric energy with the fewest fuel costs. This paper presents a new branch-and-bound algorithm for the unit scheduling problem. An efficient branching method based on the 'heap' data structure and a simple intuitive bounding rule are proposed.Computational results indicate that the presented approach locates the optimum schedule in less time than many existing techniques. INTRODUCT 1ONTo economically commit available thermal generating units under constraints is still the subject under intensive research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Costs of unit commitment are incurred both from starting up generating units and from dispatching them. The overall cost over the study period is to be minimized and the variables to be determined are the hourly statuses of generating units, namely ON(committed) or OFF(unco"itted).Constraints in the unit commitment problem can naturally be divided into two categories : the "coupling" constraints and the "local" constraints. The "coupling" constraints reflect the sum of the power generated by all units. This whole generation must meet the system demand, including network transmission losses and spinning reserves. The "local" constraints deal with each thermal unit individually. The first is the upper and lower limits on generated power, if the unit is ON. And there are technical constraints, together with the requirement of limiting equipment fatigue, leading to the imposition of minimum up times and nunimum down times.Optimal unit commitment is the cheapest production policy that se!ects the most economical start-up and shut-down times for each unit such that all constraints are satisfied for the study period. Many attempts have been made to solve this problem. References [l-41 propose solution methods based on unit priority lists and heuristic rules to improve a given feasible solution. In references [5, 92 SM 483-8 EC A paper recommended and approved by the IEEE Energy Development and Power Generation Committee of the IEEE Power Engineering society for presentation at the IEEE/Shun-Chung Wang 61 a solution methodology based on duality, Lagrangian relaxation, and nondifferentiable optimization is described. Merlin and Sandrin [7] propose another Lagrangian relaxation method: this is a decomposition method using Lagrange multipliers which provides a new solution to the conventional problem of thermal unit commitment. Dillion et al. [8] and Pang et al. [9]formulate the unit commitment problem as a linear mixed-integer programming problem and then use standard integer programming algorithms to solve for the commitment schedule. Dynamic programming has long been used by many authors to solve the unit commitment problem [lo-151. In order to keep the problem tractable, these methods assume some partial ordering which specifies which set of units can be used for dispatch at a given ...

Application of Advanced Particle Swarm Optimization Techniques to Wind-Thermal Coordination

“…This problem is further complicated by the wind-thermal coordination scheduling imposed by the adding of additional reserve requirements. Because of strong coupling between system spinning reserve requirements and the total actual wind power generation, both of them should be consider at the same time, it is very difficult to solve the wind-thermal coordination problem Conventional methods [1][2][3][4] usually assume the inputoutput characteristics of power generators, known as cost curves to be quadratic or piecewise quadratic, monotonically increasing functions. But modern generating units have a variety of non-linearities in their cost curves due to valve point loading and other effects, which make this assumption inaccurate and resulting approximate solutions cause a lot of revenue loss overtime.…”

Thermal unit commitment solution using an improved Lagrangian Relaxation

“…These methods or approaches have ranged from highly complex and theoretically complicated methods to simplified methods. In the past, various approaches such as DP [1], B&B [2] and Lagrangian relaxation (LR) [3] were proposed for solving the UCP. However, not all of these methods are regarded as feasible and/or practical as the size of the system increases.…”

“…However, not all of these methods are regarded as feasible and/or practical as the size of the system increases. For moderately sized production systems, exact methods, such as dynamic programming (DP) or branch-and-bound (B&B) [2] can be used to solve the UCP, successfully. For larger systems, exact methods fail because the size of the solution space increases exponentially with the number of time periods and units in the system.…”

Binary-Real Coded Genetic Algorithm Based <i>k</i>-Means Clustering for Unit Commitment Problem

“…Such alternative algorithms studied for the UC problem can be divided into two classes [4]: deterministic methods and meta-heuristic methods. The investigated deterministic methods include Priority List (PL) [5], Dynamic Programming (DP) [6], branch-and-bound method [7], Lagrangean Relaxation (LR) [8] and Mixed Integer Linear Programming (MILP) [9]. These methods suffer from the quality of final solution are not guaranteed, the "curse of dimensionality" if the size of a system is large, applied to small UC problems, required major assumptions that limit the solution space because it is difficult achieve a balance between the efficiency and the accuracy of the model, and may not provide feasible solutions to the relaxed problem due to the inherent non-convexity of the UC problem [10].…”