Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.
Power oscillation damping controller is designed in linearized model with heuristic optimization techniques. Selection of the objective function is very crucial for damping controller design by optimization algorithms. In this research, comparative analysis has been carried out to evaluate the effectiveness of popular objective functions used in power system oscillation damping. Two-stage lead-lag damping controller by means of power system stabilizers is optimized using differential search algorithm for different objective functions. Linearized model simulations are performed to compare the dominant mode's performance and then the nonlinear model is continued to evaluate the damping performance over power system oscillations. All the simulations are conducted in two-area four-machine power system to bring a detailed analysis. Investigated results proved that multiobjective D-shaped function is an effective objective function in terms of moving unstable and lightly damped electromechanical modes into stable region. Thus, D-shape function ultimately improves overall system damping and concurrently enhances power system reliability.