Order reduction of the dynamic model of a linear weakly periodic system-part I: general methodology

A methodology is presented for the order reduction of the dynamic model of a linear weakly periodic system obtained by linearization about the nonsinusoidal periodic steady state. It consists of two stages. First, the time-invariant part of the original full-order system is approximated by a reduced system by using singular value decomposition techniques. Then the time-varying part of the reduced system is calculated by using a Gauss-Seidel technique. The issues of sparsity, convergence, and accuracy are analyzed. The example used for illustration serves to demonstrate the efficiency of the new method.