Economic Dispatch Using the Reduced Hessian

In general, second derivative or Hessian based optimization methods have a much higher convergence efficiency than those techniques based on the gradient of the objective function. Unfortunately, for problems such as economic dispatch where the generation cost has to be minimized subject to the load flow equality constraints, the reduced Hessian with respect to the controllable variables is, in general, non-sparse and requires extensive computations to evaluate. In the literature this obstacle has been bypassed either by approximating the reduced Hessian or by handling equality constraints through penalty functions added to the cost. This last approach greatly simplifies the computation of the Hessian which also becomes sparse, but it has the drawback of requiring adjustments of the penalty functions weighting coefficients, a non-systematic step which may lead to numerical difficulties and to sub-optimal solutions.