New Numerical Integration Methods for Simulation of Electromagnetic Transients

This paper proposes two new methods of numerical integration for computation of electromagnetic transients. In the most widely used electromagnetic transients program (EMTP) trapezoidal method (TM) is employed for computation of transients. The TM has many desirable properties but in certain situations it can give rise to non-physical time step oscillations because it does not possess stiff decay property. The proposed methods effectively damp out/eliminate these oscillations. The first method is a single-step single-stage method and the second one is a single-step two-stage method. Both methods possess stiff decay property. The performance of the methods are investigated using techniques such as Z-transform analysis, magnitude and phase plots, regions of absolute stability and time-domain simulations. The investigations include comparison of results from two well-known implicit methods and an existing two-stage method. The proposed methods possess many desirable properties and can be considered for computation of electromagnetic transients and engineering problems that require stiff system computations. In addition to the above, a more efficient algorithm to include non-linear elements has been proposed for the two-stage method.

Exponential stability and numerical treatment for piezoelectric beams with magnetic effect

In this paper, we consider a one-dimensional dissipative system of piezoelectric beams with magnetic effect, inspired by the model studied by Morris and Özer (Proc. of 52nd IEEE Conference on Decision & Control (2013) 3014–3019). Our main interest is to analyze the issues relating to exponential stability of the total energy of the continuous problem and reproduce a numerical counterpart in a totally discrete domain, which preserves the important decay property of the numerical energy.