Stochastic Modelling and Stability Analysis of Large-Scale Wind Power Generation System with Dynamic Loads

As a result of dwindling fossil fuel reserves and the negative impact of greenhouse gases (GHGs) on the environment, it is important that the search for a power grid that will comprise of only variable renewable energy (VRE) generation sources such as wind or solar energy which is available everywhere for free is given much attention. The main challenge associated with these sources of energy is their variability and random nature. It is as a result of instability introduced by the VRE generation sources, that is why there is a strict control measures put in place by the regulators as to how much VRE generation sources can feed into the power grid in the case of its integration into an existing power grid. It becomes imperative to consider implications for grid stability and reliability when considering a power grid that will consist of VRE generation only. Eigenvalue approach was used to analysed the performance of anticipated large-scale VRE grid to ascertain its behaviour. Eigenvalue approach is one of the methods to examine the stability of a power system’s dynamic performance. The results indicated that it is possible to attain the necessary stability provided the assumptions made during the modelling stage is revised to improve upon the model.

On the Existence and Stability of Periodic Solutions of Airy’s Equation with Elastic Coefficients

In this paper, the existence and stability of periodic solutions of a certain second order differential equation with elastic coefficient were investigated using power series method, eigenvalue approach and lyapunov direct method. Existence of analytical solution which is independent of time was achieved using the power series method. Eigenvalue approach and Lyapunov direct method were used to investigate the stability of the resulting solution. Periodic solution was obtained using the eigenvalues of the resulting matrix. The first stability method further examined stability of the equilibrium point by considering the intervals around the origin and it’s discriminate. The equilibrium points for the intervals and the discriminate were unstable because the real part of the characteristics root is zero. Unstable equilibrium point was also obtained for the second stability method using the energy function and time derivative around the equilibrium point. The two unstable results indicated that there were highly instability regions with a strictly positive elastic coefficient. The highly instability regions were confirmed by the presence of elastic coefficient which reduces oscillation with an increase in amplitude. Furthermore, numerical simulations for existence and stability of Airy’s equation at different values of the elastic coefficient were illustrated in order to demonstrate the behaviour of the solutions which extends some results in literature.

Response of Thermoelastic Interactions in Micropolar Porous Circular Plate with Three Phase Lag Model

The present study deals with a homogeneous and isotopic micropolar porous thermoelastic circular plate by employing eigenvalue approach in the three phase lag theory of thermoelasticity due to thermomechanical sources. The expressions of components of displacements, microrotation, volume fraction field, temperature distribution, normal stress, shear stress and couple shear stress are obtained in the transformed domain by employing the Laplace and Hankel transforms. The resulting quantities are obtained in the physical domain by employing the numerical inversion technique. Numerical computations of the resulting quantities are made and presented graphically to show the effects of void, phase lags, relaxation time, with and without energy dissipation.

Elastodynamic Response of a Three-Phase-Lag Model of Orthorhombic Thermoviscoelastic Material with Reference Temperature Dependent Properties

A three-phase-lag model of a homogeneous thermally conducting orthorhombic thermoviscoelastic material under the effect of the dependence of reference temperature on all elastic and thermal parameters is investigated. The Laplace and Fourier transform and eigenvalue approach techniques are used to solve the resulting nondimensional coupled equations. As an application of the problem, harmonically varying and sinusoidal pulse functions are considered. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made for thermoviscoelastic temperature dependent, thermoviscoelastic and thermoelastic materials, respectively, for different values of time, for temperature gradient boundary.