Abstract—Large, complex dynamical systems, such as, power systems, are very challenging task to model and analysis. Numerous techniques have been developed to handle the difficulties arising from the size and complexity of typical realistic power system models. These complexities demand to formulate reduced order dynamic equivalent models of power systems in many applications and studies. Linearizing around the equilibrium point, a stable time invariant power system model leads to index 1 differential-algebraic (DAE) system. A balancing based model reduction technique for such a system is discussed in a paper of F. Freitas et al. in 2008. The main drawback of this method is to compute two Gramian factors of the system by solving two continuous-time algebraic Lyapunov equations. On the other hand interpolatory model reduction via iterative rational Krylov algorithm (IRKA) is computationally efficient since it requires only matrix-vector products or linear solvers. This paper contributes an interpolatory technique using IRKA for a class of index 1 DAE systems to obtain reduced standard ordinary differential (ODE) systems. We also show that a simple algebraic manipulation retrieve reduced index-1 DAE systems. The proposed technique is applied to a data of linearized power system models. Numerical results illustrate the efficiency of the techniques.
Index Terms—Descriptor systems, indices of descriptor systems, interpolatory projection, model reduction, power systems, rational Krylov approximation.
Mohammad-Sahadet Hossain was with Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany. He is now with the Department of Mathematics and Physics, North South University, Dhaka, Bangladesh (e-mail: mohammad.hossain@northsouth.edu).
M. Monir Uddin is with the Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, D-39106 Magdeburg, Germany (e-mail: uddin@mpi-magdeburg.mpg.de).
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Cite: Mohammad-Sahadet Hossain and M. Monir Uddin, "Reduce Order Modelling of Power System Models Using Interpolatory Projections Technique," International Journal of Modeling and Optimization vol. 5, no. 3, pp. 228-233, 2015.
