Solving Unit Commitment Problem Using Lagrange Algorithm

In this problem, we employ the Lagrange algorithm to determine the optimal unit commitment configuration for a system comprising five generating units. The Lagrange algorithm serves as an optimization technique particularly effective for constrained optimization problems. For this implementation, we transform the original constrained problem into an unconstrained formulation by incorporating constraints through Lagrange multipliers. The core computational approach involves defining the Lagrangian function L(x,λ) = f(x) + λ·g(x), where f(x) represents the objective function (typically minimization of generation costs) and g(x) denotes the system constraints (such as power balance and unit capacity limits). The algorithm proceeds by iteratively updating the primal variables (unit commitment decisions) and dual variables (Lagrange multipliers) using subgradient methods or heuristic updates. Key implementation components include penalty function handling for constraint violations and convergence criteria monitoring. Through computational optimization, we can efficiently identify the optimal unit combination that satisfies operational requirements while minimizing overall production costs.