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



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.

              Here two parameter SPM is 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.

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