Power System Optimization

Introduction to the formulation of optimization problems: Problem variables, problem constraint, the objective function. Calculus based techniques: Unconstrained Minimisation: Powell’s method of conjugate directions, Gradient methods, second order methods. Constrained Minimisation Problems: Indirect methods by unconstrained minimization, penalty function approach. Direct methods for constrained optimization; Lagrange multipliers, Kuhn Tucker conditions; methods of feasible directions. Linear (LP) and Non-linear programming. Application of LP to power systems problems economic dispatch, automatic load shedding generation expansion studies. Non-Calculus Based Methods: Guided random search techniques: Evolutionary algorithms, simulated annealing, genetic algorithms.