Abstract.In the reliability analysis of the distribution network, information entropy is considered as the measure of uncertainty. The simple mathematical model that allows determining an entropy of a network structure is offered. The model is based on Shannon's approach to the determination of information. Reliability analysis comes down to the comparison of two components of entropy: the first is the entropy of connection a sourceelectroreceiver in the structure; the second is a boundary entropy as information of observance of the requirement to support the required reliability level of electrical power supply of the electroreceiver. The example and the procedure how to perform the necessary calculations for the analysis are provided. IntroductionThe design and operation of systems of external power supply of mining enterprises are aimed to ensure the no-break operation of electroreceivers. One of the criteria of viability evaluation of the system is its reliability in electricity power supply of customers. The regular monitoring of system operation of electrical power supply, data processing and analysis allow designers and operators to develop effective solutions for compliance with a specified level of reliability.There are many schemes of electrical power supply of mining enterprises. Let's address to the schemes of radial distributive networks, which are used to internal electrical power supply of quarries (mines). Such networks have a simple structure and successfully provide the given level of structural reliability. When analyzing structural reliability of the network, the statistical indices are considered to be the most important: failure flow frequency; the recovery time of damages; the states probabilities of the network elements, etc.When performing reliability analysis of a distribution network of mining enterprises electrical power supply, then promising direction can be considered the estimation of information uncertainty about the state of the structure. The information uncertainty (its measure) is one of the criteria of the reliability evaluation of technical systems.
The model is based on the criteria of costeffectiveness and information uncertainty. The created model has fundamental difference from the current classical economicmathematical models. As constraints it is proposed to use the mathematical expressions of the information entropy determination of two states of the system: operable and nonoperable. These expressions are the constraints imposed in the task that creates an optimal radial network with redundancy. Expressions are constructed as all the elements reserving the each other are similar, i.e. they have the same performance. The given example shows how to calculate the information entropy, where a constraint is a problem solution, as well as the possibility of both applications of probabilities and numerical values for the information entropy determination is proved.
The paper considers methods for processing data on commercial losses in electric networks with subsequent analysis of the obtained results. The information processing tools included methods for determining the amount of divergence of electric power losses when comparing planned and actual data. Comparing the planned and actual values of electric power losses, a method is proposed that in the classical theory of information is called “Kullback-Leibler divergence”. The rationale for its use is based on the possibility of applying a measure of information uncertainty, where information entropy is taken as a measured value. Comparing the planned and actual values of electric power losses, discrepancies between these distributions are obtained based on the application of the Kullback-Leibler model. The obtained results not only confirmed the importance of the applicability of this method of information processing, but also allowed us to draw attention to the adequacy of the planned losses to the actual ones.
The possibility of applying the information theory in the problem of comparing the expected and statistical probability distribution of failures of a technical system are considered. The paper presents a brief analysis of the processes of additive and multiplicative growth of the system indicators, among which the probability of failure-free operation and failure rate were considered. These indicators were considered in order to analyze the reliability of the system. The increase in reliability of the indicators is associated with the fixing of the failure rate of the system elements and the construction of probability distributions. In order to compare the two distributions, a method for measuring uncertainty is proposed, which includes Shannon’s measure of uncertainty, cross-entropy and Kullback-Leibler divergence. Together, they make it possible to determine the connection between the two different probability distributions of failures, to calculate the distance between the distributions, to identify the degree of difference between the real and desired state of the system during operation. An example of calculation confirming the importance of the participation of the offered method for measuring uncertainty in the problem of comparison of the expected and statistical probability distribution of system failures is given.
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