Energy-diminishing integration of gradient systems

Using Dynamic Thermal Rating and Energy Storage Systems Technologies Simultaneously for Optimal Integration and Utilization of Renewable Energy Sources

Nowadays, optimal integration and utilization of renewable energy sources (RES) are of the most challenging issues in power systems. The wind and solar generation units' maximum production may or may not occur at peak consumption times resulting in non-optimal utilization of these resources. As a solution to this problem, energy storage systems (ESS) are embedded in networks. However, the power...

Analysis of gradient descent methods with non-diminishing, bounded errors

Implementations of stochastic gradient search algorithms such as back propagation typically rely on finite difference (FD) approximation methods. These methods are used to approximate the objective function gradient in steepest descent algorithms as well as the gradient and Hessian inverse in Newton based schemes. The convergence analyses of such schemes critically require that perturbation par...

On the long - time integration of stochastic gradient systems

Author for correspondence: B. Leimkuhler e-mail: [email protected] On the long-time integration of stochastic gradient systems B. Leimkuhler1, C. Matthews1 and M. V. Tretyakov2 1School of Mathematics and the Maxwell Institute for Mathematical Sciences, University of Edinburgh, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK 2School of Mathematical Sciences, University of Nottingham, N...

Integration of Renewable Energy into Present and Future Energy Systems

Numerical Analysis of a Robust Free Energy Diminishing Finite Volume Scheme for Parabolic Equations with Gradient Structure

We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves at the discrete level the formal gradient flow structure, allowing the use of some nonlinear test functions in the analysis. The existence of a solution to and the convergence of the scheme are proved under very general ...