A Powerful Tool for Optimal Control of Energy Systems in Sustainable Buildings: Distortion Power Bivector

Abstract

In the field of building constructions, there is undeniably a growing need to optimize the energy systems which are a key target in new modern constructions and industrial buildings. In this sense, energy systems are being traced for the development of energy distribution networks that are increasingly smart, efficient, and sustainable. Modern generation and distribution energy systems, such as microgrids control systems, are being affected by the presence of linear and nonlinear loads, resulting a distorted voltage and current waveforms. Thus, it is stated that industrial and residential building heating and cooling loads behave essentially like sources of harmonics. This paper presents a new framework based on geometric algebra (GA) to the definition of a multivectorial distortion power concept, which is represented by a bivector that is geometrically interpreted to distinguish the rotated distortion and distortion power bivectors in these kinds of loads. Both bivectors, and their relations to the phase angles of distorted voltage are the main subject of this paper to interpret an optimal control of building energy. Numerical examples are used to illustrate of the suggested distortion power concept, as well as the information it provides for energy control in new buildings in a more sustainable way.

Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

“…Essentially, heating and cooling systems in industrial and residential buildings can be considered as sources of harmonic distortions. The paper [16] presents a new concept based on geometric algebra (GA) aimed at determining the power of multivector distortions represented in the form of a bivector. Both bivectors and their relationship with the phase angles of distorted voltage are analyzed.…”

“…It should be noted that the formality of writing (55) also lies in the fact that the cancellation of the expression under the mark of "sign" is possible both at individual points of segment 0≤t≤T and in its entire sections. In this case, as a rule, the maximum principle is not sufficient to determine the optimal control; additional research is required to identify singular controls [16].…”

Current survey of Clifford geometric algebra applications

“…This is due to the identification of heating and cooling loads behavior with sources of harmonics. Indeed, in Manuel and Francisco, 47 a new framework based on GA is presented in the definition of a multivectorial distortion power concept, which is represented by a bivector that is geometrically interpreted to distinguish the rotated distortion and distortion power bivectors in these kinds of loads. Both bivectors and their relations to the phase angles of distorted voltage are the main subject to interpret an optimal control of building energy 48–50 …”