Application of Singular Perturbation Method to Two Parameter Discrete Power System Model

Abstract

The singularly perturbed systems are ill-conditioned systems exhibiting slow fast
phenomena with computational stiffness. Hence exact solution of these systems requires
special numerical methods to overcome this stiffness. Singular perturbation theory of
continuous-time control systems has reached its peak. Whereas singular perturbation theory
of discrete-time control systems is still in developing stage. Singular perturbation
methodology (SPM) is being developed for one- and multi parameter problems in discrete
control systems. The SPM removes the system’s stiffness and satisfies all the specified
boundary conditions thereby giving an approximate solution very close to the exact solution.
Two parameter SPM are presented for linear time-invariant discrete control system for
both initial and boundary value problems. Then these are applied to a fifth-order steam
power system model up to second order approximation as a case study. These results are
compared with the exact solution. This comparison justifies the application and SPM
presented.