Lagrangian heuristics based on disaggregated bundle methods for hydrothermal unit commitment

Abstract

Abstract-The paper presents a simple and effective Lagrangian relaxation approach for the solution of the optimal short-term unit commitment problem in hydrothermal power-generation systems. The proposed approach, based on a disaggregated Bundle method for the solution of the dual problem, with a new warm-starting procedure, achieves accurate solutions in few iterations. The adoption of a disaggregated Bundle method not only improves the convergence of the proposed approach but also provides information that are suitably exploited for generating a feasible solution of the primal problem and for obtaining an optimal hydro scheduling. A comparison between the proposed Lagrangian approach and other ones, based on sub-gradient and Bundle methods, is presented for a simple yet reasonable formulation of the Hydrothermal Unit Commitment problem.

Unit Commitment by Structure Based Solution and Efficient Lagrangian Relaxation

“…To overcome the "curse of dimensionality", decomposition techniques based on Lagrangian relaxation theory are generally preferred [6][7]. In these decomposition methods, the original problem is relaxed by removing the so called "complicating constraints", also known as "coupling constraints", to obtain a separable optimization problem, which can be divided into many smaller independent optimization problems, usually referred to as subproblems [8][9][10][11][12][13]. There is normally one subproblem for each unit in the UC problem, and the Lagrangian multipliers are used to coordinate the solutions of the subproblems [7].…”

“…The first step optimizes the dual function and common approaches include subgradient (SG) and cutting plane (CP) based methods [10]. This step is iterative and accounts for most of the computational cost in the whole solution process.…”

“…This step is iterative and accounts for most of the computational cost in the whole solution process. Both the SG and CP methods are plagued by slow convergence, requiring hundreds, sometimes thousands of iterations [7,10]. An important research objective has been to develop dual optimization methods with fast convergence characteristics.…”

Optimal Methods for Power System Operation and Management

“…These include network reconfiguration using optimization methods such as DP, OPF, etc [1][2][3] and UC using Lagrange and other optimization methods [4][5][6][12][13][14]. This assumes as static power system problem and also suffers from storage and burden of computation inability to handle stochasticity and dynamics of parameter changes.…”

The necessary and sufficient conditions for determining feasible solutions to unit commitment problems with ramping constraints

“…Lagrangian Relaxation (LR) is one of the most successful methods for obtaining near optimal solutions ( [1][2][3][4][5][6][7][8]), where Lagrange multipliers relax the system-wide constraints. The research of developing efficient algorithms to solve UC problems with ramp rate constraints is active ( [11][12][13][14][15][16]).…”