Load balancing for smart grid: centralized and distributed approaches

As one of the greatest concerns in the context of smart grid, the load balancing problem is addressed by improving the electrical power efficiency and stability via scheduling power loads, thereby shaping the power demand into the desired pattern. The research explores the load balancing strategies to reduce the demand fluctuations in the smart grid systems. Centralized and decentralized load balancing methodologies are discussed. For centralized approaches, offline and online exact power allocation methods are investigated by utilizing the geometric water-filling (GWF) approach. Furthermore, decentralized load balancing problem is discussed at power distribution sub-network level. Electrical vehicle (EV) fleeting among the neighbouring charging stations is considered. Load balancing for the whole grid is achieved by local optimization processes via Proximal Jacobian Alternating Direction Method of Multipliers (ADMM) technique. Overall, facilitated by our proposed strategies, the reliability of the electric grid can be enhanced.

Load balancing for smart grid: centralized and distributed approaches

As one of the greatest concerns in the context of smart grid, the load balancing problem is addressed by improving the electrical power efficiency and stability via scheduling power loads, thereby shaping the power demand into the desired pattern. The research explores the load balancing strategies to reduce the demand fluctuations in the smart grid systems. Centralized and decentralized load balancing methodologies are discussed. For centralized approaches, offline and online exact power allocation methods are investigated by utilizing the geometric water-filling (GWF) approach. Furthermore, decentralized load balancing problem is discussed at power distribution sub-network level. Electrical vehicle (EV) fleeting among the neighbouring charging stations is considered. Load balancing for the whole grid is achieved by local optimization processes via Proximal Jacobian Alternating Direction Method of Multipliers (ADMM) technique. Overall, facilitated by our proposed strategies, the reliability of the electric grid can be enhanced.

Lie Symmetry Analysis, Conservation Laws, Power Series Solutions, and Convergence Analysis of Time Fractional Generalized Drinfeld-Sokolov Systems

In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fractional differential operator, the time fractional GDSS equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. Moreover, we have constructed conservation laws for time fractional GDSS and obtained explicit power series solutions of the reduced nonlinear ODEs that converge. Lastly, some figures are presented for explicit solutions.

A formula for hidden regular variation behavior for symmetric stable distributions

We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates in “different directions”, illustrating the phenomenon of hidden regular variation. We give several examples and obtain quite varied behavior, including sets which do not have exact power-law decay.

Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation

To discuss the invariance properties of a sixth-order generalized time-fractional Sawada-Kotera equation, on the basis of the Riemann-Liouville derivative, the Lie point symmetry and symmetry reductions are derived. Then the power series theory is used to construct the exact power series solution of the equation. Finally, the conservation laws for a sixth-order generalized time-fractional Sawada-Kotera equation are computed.

A comparative study of some cosmological models with time varying G and Λ: A symmetry approach

We study how the constants G and Λ may vary in four different theoretical models: general relativity with time-varying constants (Y.-K. Lau. Aust. J. Phys. 38, 547 (1985). doi: 10.1071/PH850547 ), the model proposed by Lu et al. (Phys Rev D, 89, 063526 (2014). doi: 10.1103/PhysRevD.89.063526 ), the model proposed by Bonanno et al. (Class. Quant. Grav. 24, 1443 (2007). doi: 10.1088/0264-9381/24/6/005 ), and the Brans–Dicke model with Λ([Formula: see text]) [ 25 ]. To carry out this study, we work under the self-similar hypothesis and we assume the same metric, a flat Friedmann–Robertson–Walker metric, and the same matter source, a perfect fluid. We put special emphasis on mathematical and formal aspects, which allows us to calculate exact power-law solutions through symmetry methods, matter collineation, and Noether symmetries. This enables us to compare the solutions of each model and in the same way to contrast the results with some observational data.