scholarly journals Short-term Hydro-thermal Coordination By Lagrangian Relaxation: A New Algorithm for the Solution of the Dual Problem

2020 ◽  
Author(s):  
Pedro Bento ◽  
Filipe Pina ◽  
Sílvio Mariano ◽  
Maria do Rosario Calado
Keyword(s):  
Lagrangian Relaxation ◽  
Lagrange Multipliers ◽  
Large Scale ◽  
Dual Problem ◽  
Unit Commitment ◽  
Subgradient Methods ◽  
Step Size ◽  
Coordination Problem ◽  
Unit Commitment Problem ◽  
Primal Problem

For decades, researchers have been studying the unit commitment problem in electrical power generation. To solve this complex, large scale and constrained optimization (primal) problem in a direct manner is not a feasible approach, which is where Lagrangian relaxation comes in as the answer. The dual Lagrangian problem translates a relaxed problem approach, that indirectly leads to solutions of the original (primal) problem. In the coordination problem, a decomposition takes place where the global solution is achieved by coordinating between the respective subproblems solutions. This dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. To tackle, time-consuming tuning tasks  or user related experience, a new adaptative algorithm, is proposed to better adjust the step-size used to update Lagrange multipliers, i.e., avoid the need to pre-select  a set of parameters. A results comparison against a traditionally employed step-size update mechanism, showed that the adaptive algorithm manages to obtain improved performances in terms of the targeted primal problem. Keywords: Hydro-Thermal coordination, Lagrangian relaxation, Lagrangian dual problem, Lagrange multipliers, Subgradient methods

scholarly journals A Novel Lagrangian Multiplier Update Algorithm for Short-Term Hydro-Thermal Coordination

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6621
Author(s):  
P. M. R. Bento ◽  
S. J. P. S. Mariano ◽  
M. R. A. Calado ◽  
L. A. F. M. Ferreira
Keyword(s):  
Lagrange Multipliers ◽  
Large Scale ◽  
Dual Problem ◽  
Electrical Power ◽  
Decomposition Methods ◽  
Subgradient Methods ◽  
Lagrangian Multiplier ◽  
Step Size ◽  
Primal Problem ◽  
Require Time

The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem.

Absolutely Stochastic Simulated Annealing Approach to Large Scale Unit Commitment Problem

2006 ◽  
Vol 34 (6) ◽  
pp. 619-637 ◽  
Author(s):  
Tomonobu Senjyu ◽  
Ahmed Yousuf Saber ◽  
Tsukasa Miyagi ◽  
Naomitsu Urasaki ◽  
Toshihisa Funabashi
Keyword(s):  
Simulated Annealing ◽  
Large Scale ◽  
Unit Commitment ◽  
Unit Commitment Problem ◽  
Scale Unit ◽  
Commitment Problem

scholarly journals A Novel Strategy to Reduce Computational Burden of the Stochastic Security Constrained Unit Commitment Problem

Energies ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3777
Author(s):  
Cristian Camilo Marín-Cano ◽  
Juan Esteban Sierra-Aguilar ◽  
Jesús M. López-Lezama ◽  
Álvaro Jaramillo-Duque ◽  
Juan G. Villegas
Keyword(s):  
Decision Making ◽  
Power Systems ◽  
Large Scale ◽  
Unit Commitment ◽  
Reaction Times ◽  
Mixed Integer ◽  
Feasible Region ◽  
Solution Strategy ◽  
Unit Commitment Problem ◽  
Joint Strategy

The uncertainty related to the massive integration of intermittent energy sources (e.g., wind and solar generation) is one of the biggest challenges for the economic, safe and reliable operation of current power systems. One way to tackle this challenge is through a stochastic security constraint unit commitment (SSCUC) model. However, the SSCUC is a mixed-integer linear programming problem with high computational and dimensional complexity in large-scale power systems. This feature hinders the reaction times required for decision making to ensure a proper operation of the system. As an alternative, this paper presents a joint strategy to efficiently solve a SSCUC model. The solution strategy combines the use of linear sensitivity factors (LSF) to compute power flows in a quick and reliable way and a method, which dynamically identifies and adds as user cuts those active security constraints N − 1 that establish the feasible region of the model. These two components are embedded within a progressive hedging algorithm (PHA), which breaks down the SSCUC problem into computationally more tractable subproblems by relaxing the coupling constraints between scenarios. The numerical results on the IEEE RTS-96 system show that the proposed strategy provides high quality solutions, up to 50 times faster compared to the extensive formulation (EF) of the SSCUC. Additionally, the solution strategy identifies the most affected (overloaded) lines before contingencies, as well as the most critical contingencies in the system. Two metrics that provide valuable information for decision making during transmission system expansion are studied.

scholarly journals An Improved Subgradiend Optimization Technique for Solving IPs with Lagrangean Relaxation

2013 ◽  
Vol 61 (2) ◽  
pp. 135-140
Author(s):  
M Babul Hasan ◽  
Md Toha
Keyword(s):  
Dual Problem ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Concave Function ◽  
Optimization Method ◽  
Duality Gap ◽  
Dual Function ◽  
Subgradient Optimization ◽  
Step Size ◽  
Primal Problem

The objective of this paper is to improve the subgradient optimization method which is used to solve non-differentiable optimization problems in the Lagrangian dual problem. One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of step-lengths to update successive iterates. In this paper, we propose a modified subgradient optimization method with various step size rules to compute a tuning- free subgradient step-length that is geometrically motivated and algebraically deduced. It is well known that the dual function is a concave function over its domain (regardless of the structure of the cost and constraints of the primal problem), but not necessarily differentiable. We solve the dual problem whenever it is easier to solve than the primal problem with no duality gap. However, even if there is a duality gap the solution of the dual problem provides a lower bound to the primal optimum that can be useful in combinatorial optimization. Numerical examples are illustrated to demonstrate the method. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17059 Dhaka Univ. J. Sci. 61(2): 135-140, 2013 (July)

Sign in / Sign up

Export Citation Format

Share Document