Improving Lagrangian Relaxation Unit Commitment with Cuckoo Search Algorithm Hossein Zeynal 1 , Lim Xiao Hui 2 , Yap Jiazhen 2 , Mostafa Eidiani 3 , Brian Azzopardi 4 1 School of Engineering, KDU University College, Damansara Jaya, 47400 Petaling Jaya, Malaysia 2 Department of Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, UK 3 Khorasan Institute of Higher Education, Mashhad, Iran 4 Malta College of Arts, Science & Technology (MCAST),Triq Kordin, Raħal Ġdid, Malta 1 h.zeynal@kdu.edu.my, 3 eidiani@khorasan.ac.ir, 4 brian.azzopardi@ieee.org Abstract- In many utilities, it is essential to devise an optimum commitment solution of generating units for better operational efficiency, under empirical conditions. Among the methods reported in the technical literatures, Dynamic Programming (DP), Lagrangian Relaxation (LR), and Mixed-Integer Programming (MIP) are the most industry proven algorithms in the line of business. This paper improves the available solution offered in LR technique, which was mainly suffered from high fluctuation of duality gap between the primal and dual solutions. As a remedy, a Cuckoo Search Algorithm (CSA) is proposed to optimize the gap progress throughout the LR solution process. Simulation results reiterate that the developed LR-UC integrating CSA enhances the solution quality. I. INTRODUCTION Unit Commitment (UC) has a primordial role in power system operation to optimally commit and dispatch thermal and hydro generation plants throughout the scheduling horizon, in the most economical manner, subject to system- wide constraints and practical operation limits [1]. Efficient allocation of water resources associated with multiple river systems, especially in countries with limited hydropower resources, can largely affect total operation cost of the system as well as fuel utilization. UC is essentially a large-scale, nonlinear, non-differentiable, nonconvex mixed-integer mathematical programming problem with a complex constraint set [2]. In presence of detailed hydraulic modeling of the river and reservoirs, the UC problem becomes even more complex, involving an increased number of binary variables and coupling constraints. Due to the intricacy of the problem, particularly for systems of practical sizes, hatching consistent optimal schedules have proved to be extremely difficult and time-consuming. A number of solution approaches, that tend to make some simplifying assumptions, to downscale the complexity arising from the combined consideration of thermal and hydro plants, are proposed in the literature. Amongst these, the most widely used approaches by utilities are Dynamic Programming (DP) [3], [4] Lagrangian Relaxation (LR) [2], [5] and Mixed- Integer Programming (MIP) methods [6], [7]. Lagrangian Relaxation (LR) decomposes the UC problem into several subproblems [2], whereas the solution of each subproblem is coordinated through Lagrange multipliers. The subproblems are mainly solved by the DP [8] or a network flow technique [9]. Mixed-Integer Programming (MIP) technique using Branch and Cut (B&C) method was applied to the UC problem as well [6]. DP becomes numerically unstable as the dimension of the problem massively increases with the problem size [3]. Since the commitment process in the LR is carried out for individual units, modeling of the coupling constraints introduces many challenges to the solution. While the LR does not suffer from the curse of dimensionality, as with the DP, unnecessary commitment of units may occur [8], resulting in higher production costs. Furthermore, it requires many heuristic reasoning to meet the duality gap. The LR is fast, albeit rendering suboptimal solutions. Although, the LR is the preferred choice of many utilities around the world, it provides an inferior performance in terms of coupling constraints [2]. The MIP outperforms the DP and LR techniques by the direct mathematical modeling of the coupling constraints without any heuristic reasoning. Nonetheless, the broad application of the MIP is limited by the large computational requirements of an actual utility system [8]. Moreover, a larger system with complicating constraints, creates a huge number of nodes in the BB&C search-tree; making the solution time substantially long. The nonlinear MIP based UC model can further be simplified. A piecewise approximation process was employed throughout the model to convert all associated nonlinearities into an equivalent linear model. As a result, a very powerful large-scale MILP BB&C solver such as CPLEX can be used [8-10]. Comparison over these industry-size techniques has manifested that the LR technique still offers satisfactory solution (high-speed) although suffering from large fluctuation of gap and its uncontrollability at the premise of system-wise constraints. As a remedy, evolutionary search algorithms, such as Genetic Algorithm (GA), Particle Swarm Intelligence (PSI) can provide stochastic way of non-linear optimization which is inspired by biologically advancement in the nature. The 978-1-4799-7297-5/14/$31.00 ©2014 IEEE 2014 IEEE International Conference Power & Energy (PECON) 77