The increase of receivers' capacity and intensification of their work regimes lead to the distortion of the parameters of electrical energy, which, in turn, negatively affects the work of other receivers and the network itself. Electromagnetic compatibility (EMC) ensuring is associated with significant costs, which determine high requirements for accuracy and validity of EMC estimation methods in electrical networks.
Overestimation of EMC leads to unnecessary investment increase and its understatement – to the detriment of the additional power losses, reducing the life of electrical equipment, deterioration of product quality.
Relevance of the subject. Analytical solutions of nonlinear EMC problems are usually absent. To get them it is necessary to use statistical simulation (imitation) of random processes, computer methods of which are not developed enough.
Connection with academic plans, themes and programmes. The present work is performed under the plan of the Ukrainian National Academy of Sciences – Gostema № H-30-05 on the coordinating plan of Ukrainian NAS on "Scientific bases of power industry".
The object of the present work is development of the program performing statistical simulation of stationary random processes characteristic for electrical networks for further use in studies of EMC.
The idea of the work. Normal random process is a common mathematical model of the current and voltage time change in electrical networks. One of the advantages of a model like this – the possibility of using a simple apparatus of the correlation theory.
Analytical methods can determine the estimated value of EMC performance (peak performance, vibrations etc.) without calculating a realization of the processes, but they are not always sufficient for solving the problems of power supply, especially those which are non-linear: voltage regulation, reactive power regulation, the use of stabilizers, compensators, relay devices. Moreover, obtaining the necessary background information for their use sometimes is more difficult than the solving itself. In connection with this they pass to the simulation of random processes realizations with subsequent estimation of desired characteristics by them. This approach is called "statistical simulation" (in the literature the next terms are used: the method of statistical tests, the Monte Carlo method).
The source characteristics for simulation are known from experiments or technological calculations (most often – the distribution and the correlation function (CF)). If desired characteristics are analytically expressed by way of using original characteristics, then to justify the correctness of modelling it is sufficient to check the derived realizations on the accuracy of reproduction of the given characteristics. In this case, statistical simulation is equivalent to the result of the probabilistic one and replaces experimental studies.
Main tasks of research and developments: study and comparison of existing methods for statistical simulation of stationary random processes, development of the program, making it possible to obtain realizations of stationary random processes with different correlation functions, creating a user environment for easy and efficient work with the program, further use of the results.
Subject of research and developments – statistical simulation of stationary random processes with different CF.
Object of research and developments – statistical dynamics of power supply systems, electromagnetic compatibility in electrical networks.
Methodology and methods of research: in the research existing methods of statistical simulation of stationary random processes are examined, but the program implements the so-called relay-race method.
The scientific novelty of this work is in the implementation of the statistical simulation of stationary random processes similar to processes occurring in electrical networks with different CF in the user-convenient way.
Practical significance of results. The developed program will solve various problems of EMC (particularly – the development of methods for studying the effectiveness of improving the quality of electroenergy means) without resorting to experimental studies.
Testing of work. The work was performed by the report on the Ukrainian student scientific conference "Electrical and electromechanical systems".
Review of research and developments on the subject. Questions of EMC and particularly – the statistical simulation of random processes in electrical networks are engaged by Kourennyi E. G., Dmitrieva E. N, Pogrebnyak N. N. in DonNTU.
In 1999 Pogrebnyak N. N. defended the Candidate's dissertation on the topic: "The quadratic inertial smoothing in the calculation of loads of industrial electrical networks", which dealt with the above-mentioned relay-race method.
In 2008 Master Drozd V. A. investigated the possibility of simulating a random process with a given CF by passing a series of random ordinates through a linear system. The investigations showed that the method was theoretically correct, but did not give high accuracy in computer implementation. This result can be explained by the fact that the sequence of random ordinates differs from the white noise, which in principle is practically impossible to reproduce.
In 2009 Master Grusin S. A. investigated the elemental processes method for simulation of stationary random processes with exponential CF.
Issues related to power quality in electrical networks are widely reflected in the works of such domestic and foreign scientists as Zhezhelenko I.V., Liutyi A.P., Kayalov G.M., Kuznetsov V.G., Kourennyi E.G., Dmitrieva E. N., Shidlovskii A.K. and others.
The problems of stationary random processes modeling are studied by scientists of the Baltic State Technical University (Byzov L.N. and others).
The absence of deterministic relations between receivers defines the randomness of processes in electrical networks. This explains the usefulness of statistical methods for analyzing processes in systems of power supply and EMC among others. [1, p. 5]
The process is stationary if its probabilistic characteristics do not depend on the origin: the expectation and variance are constant, CF depends only on the distance between the sections &tau = t2 — t1.
More details about the theory of random processes – in [2, 3, 4, 5].
Statistical simulation allows us to create a "library of realizations" with known characteristics. This library enables us to test the effectiveness of various engineering solutions in comparable circumstances.
From the practical point of view it is desirable to build models of processes in relative units (r.u.) so that the same implementation can be used to solve various problems by changing only the scale of the coordinate axes.
The literature on simulation techniques is very voluminous (for example, [6, 7]). When choosing the method of simulating its conformity with physical conditions of the problem and laboriousness are taken into account (especially the suitability for taking into account various restrictions).
In this paper the elemental processes method, the time-quantization method and the relay-race method are examined.
Since simulating is an effective way to solve nonlinear problems of power supply, in this master's work various methods of statistical simulation of stationary random processes in electrical networks are examined.
The universal library of the realizations of typical processes in electrical networks can be used when developing effective means of improving power quality research methodology.
A choice of a model is determined by the amount of background information: when the correlation function is fully specified, it is reasonable to apply the summation of elemental processes, when it is given partially – the time-quantization method. To improve the quality of modeling using other methods or as a standalone method the relay-race method can be used. In this paper the latter one is realized by the program.
On the moment of writing this abstract the master's work was not completed. Its final variant can be obtained from the author or the scientific adviser after December 2010.