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The basis of the Energy Structure Theory can be introduced in references [1-5] presented in 2020. Energy Structure Theory explains some new thermo-physical concepts including energy space, energy structure equation, dependent and independent energy components, irreversibility components, irreversibility structure, etc. Since this theory is presented considering the first and second laws of thermodynamics as well as energy components of the system as the basis of the energy structure equation, this theory can be expanded for a variety of the scientific applications. For example, in this note, we will try to introduce some of these scientific applications in general physics and engineering analysis. Also, using relevant concepts, 2D viscoelasticity problems will be studied. Also, the viscoelasticity and kinematic energy will be calculated for 2D viscoelasticity problems. Energy structure theory let us to study physical processes from the perspective of the componential energy exchange as well as independent and dependent energy component concept introduced by this theory.

Modeling and investigating of energy distribution especially the wasted one is very important in viscoelastic problems. In this article, an applied energy model based on separation of energy components of the system is extracted and expanded to apply in linear viscoelastic problems, although this method is applicable in nonlinear problems as well. It is assumed that the whole energy of the system can be divided into two parts: Residual and non-inertial energies. The non-inertial energy is the sum of the energies that do not depend on the inertia of the system, while residual energy is the remaining of total energy. When an amount of energy is applied to the system, by determining the non-inertial energy from a novel energy conservation equation, the residual energy can be calculated. Some basic viscoelastic examples are investigated and obtained results will be compared with the expected ones.

This paper presents a macroscopic applied innovate modeling to study the performance effects of the second law of thermodynamics on the mechanical systems. To investigate the irreversibility in mechanical systems, the energy structure of the system can be studied. Some energy components relate to the reversible processes and remaining relate to the irreversible process. Exiting models are based on the studying sub structures and therefore, need a large volume of the calculations. In this paper, at first, using a macroscopic quasi-statistical approach, a new energy structure equation is extracted and by examining it’s variation in the different paths, the irreversible components as well as their structures are studied. Using the kinematic theories of dissipated energy, it can be concluded that the extracted equations have the same base as the different formulations of the second law of thermodynamics. Finally, as a mechanical system example with the possibility of irreversibility in the possible performed processes, the extracted equations are developed for viscoelasticity problems. And also the matching of the results with expected results is shown.

Growing penetration of distributed energy resources (DER) leads to emerging changes and issues in future power systems. A system oprator aims to maximise demnad side energy trading while minimising energy improts from upstream grid. This paper proposes a reliable local energy market (LEM) trading mechanism in which consumers and prosumers can trade self-produced energy in a multiple community-based market (MCBM) framework to optimally provide the balance. The proposed framework intends to maximise social welfare by fair allocation of resources, increasing the provided reserve for the main grid, and shaving the peak power resulting in enhancement of network flexibility. The overall model is formulated in the style of a bi-level problem in which the lower-level clears the market and the upper-level is designated to redistribute the costs and benefits among market participants. Furthemore, the conditional value at risk (CVaR) approach is employed to evaluate how risk affects social welfare. Moreover, the impact of multiple communities and joint energy trading on the outcomes of the market is examined. The proposed model has been evaluated by analysing IEEE 33-bus standard test system, and numerical studies verify the effectiveness of the proposed approach.