Asymptotic approximation method of optimal control applied to a power-system problem

A single machine power system connected to an infinite bus with both voltage regulator and speed governor controls is considered. This system mathematically can be described by an 8th-order nonlinear time-delay model. However, by perturbing a small scalar parameter, this 8th-order model can be reduced to a 3rd-order ordinary model without any pure time delays. An asymptotic approximate solution is constructed with respect to the scalar parameter for the 8th-order time delay model by using the solution of only the 3rd-order ordinary model. Numerical results indicate that the asymptotic solution is close to the optimal solution. Computationally, the asymptotic method is compared with the 2-variation method and is shown to be superior.