Enhanced Merit Order and Augmented Lagrange Hopfield Network for Transmission Constrained Unit Commitment Vo Ngoc Dieu, Weerakorn Ongsakul, and Wichit Krueasuk Energy Field of Study School of environment, Resources and Development Asian Institute of Technology, Pathumthani 12120, Thailand Email: ongsakul@ait.ac.th ABSTRACT This paper proposes an enhanced merit order (EMO) and augmented Hopfield Lagrange neural network (ALH) for solving transmission constrained unit commitment (TUC) problem. The EMO is a merit order enhanced by a heuristic search algorithm based on the average production cost of generating units for unit scheduling, and the ALH is a continuous Hopfield network whose energy function is based on augmented Lagrangian relaxation for economic dispatch. For each hour with insufficient power due to transmission constraint, a repairing strategy based on heuristic search is used to satisfy the constraints. The proposed EMO-ALH is tested on the 24 bus IEEE reliability test system with 26-unit and 32-unit cases and compared to decomposition and co-ordination algorithms (DCA) and three-phase algorithm scheme (TAS), respectively. The proposed method can obtain less expensive cost than the others in a faster computing time. NOMENCLATURE a i , b i , c i Coefficients of fuel cost function of unit i. A mj Generation shift distribution factor, representing power change on line m with respect to power change at bus j. D mi Sensitivity coefficient for line m flow with respect to power output of unit i. D mr Representation of power flow on line m with respect to power generation at reference bus r. I i t Congestion index of off unit i at hour t. M t Number of congested lines at hour t. N Total number of units. N G Number of buses with generation. N L Number of transmission lines. P D t System load demand at hour t, in MW. P i,max Maximum output power of unit i, in MW. P i,min Minimum output power of unit i, in MW. P i t Generation output of unit i at hour t, in MW. P m,max Maximum power flow limit of transmission line m, in MW. P m t Power flow on transmission line m at hour t, in MW. P R t System spinning reserve at hour t, in MW. R t Excessive spinning reserve at hour t, in MW. S i t Start up cost of unit i at hour t, in $. T Schedule time horizon for UC, in h. T i,down Minimum down time of unit i, in h. T i,up Minimum up time of unit i, in h. T i t ,off Continuously off time of unit i, in h. T i t ,on Continuously on time of unit i, in h. U λ t , U γm t Total input of continuous neuron corre- sponding to output of V λ t , V γm t . U i t Status of unit i at hour t (on = 1, off = 0). U i t ,H Total input of continuous neuron corre- sponding to output of V i t ,H . U m t ,H Total input of continuous neuron corre- sponding to output of V m t ,H . V λ t , V γm t Outputs of multiplier neurons representing Lagrangian multiplier λ t and γ m t , respectively. V i t ,H Output of continuous neuron representing for output power P i t . V m t ,H Output of continuous neuron representing for transmission power flow P m t . β t , β m t Penalty factors associated with power balance and transmission constraints, respectively. χ i , δ i , γ i Coefficients of start up cost function. λ t , γ m t Lagrangian multipliers associated with power balance and transmission constraints, respectively. 1. INTRODUCTION Unit commitment (UC) is used to schedule generators such that the total production cost of the system is minimized while maintaining sufficient spinning reserve and satisfying generator constraints. Many optimization methods have been proposed to solve unit commitment problem given in biography survey by Padhy [1]. Several classical methods for UC problem include priority list [2], dynamic programming (DP) [3], mixed integer programming (MIP) [4], Lagrangian relaxation (LR) [5], etc. The LR method is an appropriate coordination technique for generating feasible primal solutions while minimizing the duality gap. However, due to the non-convexity of the UC problem, optimality of the dual problem does not guarantee the feasibility of the primal UC problem. The duality gap is used to estimate the quality of the suboptimal solution. Recently, AI techniques applied to UC problem include neural network [6], simulated annealing (SA) [7], tabu search (TS) [8], genetic algorithm (GA) [9], evolutionary programming (EP) [10], etc. However, these methods require a considerable amount of computational time for large-scale problems. Since generating units of an electric utility system usually located in different areas interconnected via transmission lines, power flows are also subject to thermal limits of transmission lines in UC problem. Therefore, UC problem without transmission constraint