Process Modeling for Energy Usage in "Smart House"

Page 1

Mechanics, Materials Science & Engineering, December 2016

Process Modeli

ISSN 2412-5954

ystem with a Help of 10

Markov Discrete Chain

Victor Kravets1,a, Vladimir Kravets2, Olexiy Burov3 1

National Mining University, Dnipro, Ukraine

2

Dnipropetrovsk National University of Railway Transport, Dnipro, Ukraine

3

Jack Baskin School of Engineering, University of California-Santa Cruz, CA, USA

a

prof.w.kravets@gmail.com DOI 10.13140/RG.2.2.34948.32643

Keywords: smart house, Markov discrete chains, possible states, transition probabilities matrix, transition costs matrix, mathematical expectations of transitions costs, cost of Markov random process.

ABSTRACT. Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of "Smart house", consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the "smart house" system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.

Introduction. The issue in question relates to the problem of smart house engineering for establishing controlled process of energy usage. In this research area, there are such works as [1-3]. In this problem, the leading role belongs to establishing a mathematical model of random processes of energy usage by essential appliances, the model being adequate to physical picture. In order to establish a mathematical model for the problem in question, fundamental results of probability theory and mathematical statistics [4-6], operational research [7], especially Markov random processes theories [8,9] are used. Exploring dynamics of energy usage process in residential house implies also working out an appropriate dynamic model, process scheme, method for modeling process, computation algorithm and an appropriate software package. Dynamic model for energy usage process. Typical residential house (set of rooms) is being explored. Its essential services are provided with a help of several electrical appliances. It means that a technical system consists of independently functioning subsystems (elements). For example, let us suppose for the sake of simplicity the in the considered household there are three ( ) elements: refrigerator ( ), microwave oven ( ), light source ( e3 ). It is to mention that generalizing the

10

The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/

MMSE Journal. Open Access www.mmse.xyz

84


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.