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Abstract

Сontent

Introduction

Adequately to estimate parameters of quality of the electric power [1], it is necessary to create models which would reflect the basic properties of objects, barriers, reactions to barriers. In the literature influence of asymmetry is estimated on following parameters EMC: to temperature of additional overheating, frequency rate of decrease in service life of isolation and additional losses of active capacity. Depending on the created model, distinguish static and dynamic parameters ENC. In statistical models reaction and a barrier are connected by functional dependence, but such models approach only for slowly changing processes or not changing absolutely not. In dynamic models target process is connected with a barrier differential or integrated the equations and such models are applied to the description быстроменяющихся processes. In [2] dynamic models ENC on asymmetry voltage in which inertial links which model heating an electric equipment join existing statistical models are developed. Different sensitivity of different electric receiver’s asymmetry is considered by factors of transfer on temperature and losses of active capacity.

The urgency of subject matter - one of making dynamic models of electromagnetic compatibility (EMC) is the block of square-law inertial smoothing (SIS) of reaction of electric receivers or the person on barriers EMC. Nonlinearity of a problem concerning to SIS does not allow to find the analytical decision. The existing approached decision in the form of some Edgeworth with the limited quantity composed not is correct. Methods of imitation of accidental barriers EMC allow defining "skilled" numerical characteristics on an output of SIS.

Purpose of work - development of methods of calculation of parameters of quality of the electric power on the basis of imitation of entrance processes.

The primary tasks of development and researches:

  • An assessment of a condition of a question
  • Imitation of accidental processes with the set characteristics
  • Calculation of inertial parameters EMC

Object of development and researches - accidental processes of variation of a pressure in electric networks.

Procedure and methods of researches - methods of statistical dynamics of electric networks.

Scientific novelty - reception of dependences of parameters of quality of the electric power (PQEP) on an output of dynamic models of objects from characteristics of processes input an accidental barrier.

Practical significance of the received results - a procedure of assessment PQEP at accidental influences at absence of the analytical decision.

The review of researches and development on subject matter. Questions of concept and maintenance of quality of the electric power in electric networks are widely reflected in works of such foreign and domestic scientists as Zhezhelenko I., Lutiy A., Кayalov A., Kuznecov V.,, Kurennyj E., Dmitrieva E., Shidlovskij A., etc.

In Zhezhelenko I.V., Saenko J.L. book Parameters of quality of the electric power and their control over the industrial enterprises are considered questions of normalization of quality of the electric power, methods of calculation and normalization of parameters of quality of the electric power, questions of standardization in the SIS and the countries of abroad are generalized. The comparative analysis of the international standards is resulted, problems of a failure of a pressure are considered, consideration of methods and means of improvement PQEP, currently available methods of measurements is expanded. The special attention is given to economic and legal aspects of a problem of quality of the electric power and methods of its optimization.

In the book of Kuznecov V., Kurennyj E., Ljutyj A. Electromagnetic compatibility. Asymmetry and nonsinusoidality a voltage main principles of construction of dynamic models of an electric equipment for estimation EМС on asymmetry and nonsinusoidality voltage are stated. Parameters EМС reflecting additional heating and reduction of service life of an electric equipment, as well as loss of active capacity are established. Methods of calculation and measurement of dynamic parameters EМС for various cases of the initial task are offered. The direction of perfection of standards by normalization of dozes of asymmetry and nonsinusoidality [3] is specified.

In monography of Shidlovskyi A., Kuznetsov V. «Improvement of quality of energy in electric networks» methods and means of improvement of quality of the electric power in modern systems of electrosupply are considered. Bases of the theory, principles of construction and questions of application single-and multipurpose static arrangements of correction of parameters of quality of the electric power in electric networks with the isolated neutral and a zero wire are stated at availability of asymmetrical and nonlinear loads. Methods of an optimum choice of parameters and installation sites of arrangements in networks are resulted at the determined and accidental characters of variation of parameters of loads. For scientific and the technical officers, prosecute subjects of improvement of quality of the electric power, optimization of modes of electric networks, development of static sources of the jet capacity, symmetrizing arrangements, power filters, as well as design and operation of modern systems of electrosupply [9].

In book Аrrilaga G. «Harmonics in electric systems» are considered sources of the maximum harmonics in electric networks, their influence on technical - economic characteristics of work of various electroreceivers and on communication lines, ways of their measurement, calculation on the computer and a choice of means of their suppression. Are resulted the information on normalization of harmonics in the various countries.

In the manual for NGТU under Vagin G., Loskutov A., Sevostjanov A. authorship « Electromagnetic compatibility in electric power industry» the theory and methods of construction of systems of electrosupply in view of electromagnetic compatibility of electroreceivers are considered. The analysis of types electromagnetude the barriers created by electroreceivers is given, their mathematical models are resulted. Influence of barriers on various electroreceivers, control systems and relay protection is shown. Methods of calculation and forecasting electromagnetude barriers are stated.

In questions EМС and modelling of accidental processes in electric networks in DonNTU are engaged prof. Kurennyj E., prof. Dmitrieva., doc. Pogrebnjak N.N.

In 2010 master Ivko E. in the master’s work «Statistical modelling of stationary accidental processes in electric networks » considered and compared methods of modelling of stationary accidental processes on the basis of what for creation of program StaSim, the go-ahead method has been chosen. In Microsoft Visual C++ environment program StaSim which with high accuracy reproduces the law of distribution and correlation function of accidental process has been developed. There was imitation a barrier of a current through the condenser at not sine wave pressure, inertial square-law smoothing by means of the simulated process is executed. The developed program has been entered into educational process in a rate for masters in discipline «EМС».

Prokhorov S. is engaged in the description and modelling of accidental processes in the book «The Mathematical description and modelling of accidental processes» it considers methods of the description, algorithms and software of generating of accidental processes, streams of events, noneqvidistating temporary numbers with the set likelihood characteristics, as well as methods and means of an assessment of quality the generating based on approximation the approach and the analysis of phase portraits. The description of the developed automated information systems for generating and аpproximation the analysis of accidental processes, temporary numbers [11] is resulted.

In the Moscow scientific magazine «Transport and Power » academies of sciences of the USSR, 1977 Kurennyj E., Dmitrieva E. article «Statistical modelling of normal processes in factory electric networks» are considered ways of modelling of normal processes in the electric networks, providing the necessary accuracy on sites of the limited duration. Modelling is carried out at in full or in part set correlation function. Characteristics and microstructures of models are compared. The indispensability of use of relative units is found out. Ways of definition of the minimal duration of modelled processes are specified. On an example of arc steel-smelting furnaces application of modelling to the decision of problems of an assessment of quality of a pressure [10] is illustrated.

In 1999 docent Pogrebnjak N. has protected the master's thesis on subject matter: « Methods of square-law inertial smoothing in calculations of loads of industrial electric networks» in which methods of imitation of realizations of the accidental electric processes providing reproduction of the set law of distribution of probabilities and correlation function are offered. The method of statistical modelling solves a problem of definition of the statistical law of distribution of a square accidental an electric load after inertial smoothing. On the basis of the received statistical decision it is developed more precise engineering methods of definition of the rated electric loads, allowing to raise efficiency of capital investments and functional reliability of industrial electric networks. The way of definition of parameter exponential is offered to correlation function of the group chart of an electric load [7].

In 2008 master Drozd V. in master’s work «Square-law inertial smoothing in models of electromagnetic compatibility », investigated a possibility of imitation of accidental process with set CF by passing consistently accidental ordinates through linear system. For example, for reception of process with exponential CF accidental ordinates are passed through a RC-circuit which constant to time it is equal given to time of correlation.

The executed researches have shown, that this theoretically proper method does not give high accuracy at computer realization. It speaks that the sequence of accidental ordinates differs from white noise which basically practically cannot be reproduced. In this connection the method of elementary processes [8] further is applied.

In 2009 master Gruzin S. in master’s work «Inertial parameters of electromagnetic compatibility » were used with a method of elementary processes for modelling accidental stationary processes with exponential CF. In the given work random numbers with exponential distribution have been received, imitation is lead and its correctness and accuracy of reconstruction of elementary process with exponential CF, imitation the sum of elementary processes is checked up, checked up КФ and normal distribution. Estimation qualities of imitation it has been lead by means of a method of confidential intervals. As a result of work dependences of inertial maxima and minima of the smoothed group chart on parameter CF have been constructed.

Dynamic models EMC on asymmetry of voltage

In static model EMC for estimation the temperature of additional overheating from asymmetry is necessary to add the inertial link with individual factor of transfer and constant inertia T. Generally dynamic model EMC of one electric receiver contains weighing filter (WF) and the block of square-law inertial smoothing (SIS) (fig. 1.1)a, and WF any more will not be a proportional link as in static model. On the proportional block 4 with factor of transfer acts square-law currently inertial process [3].

Block diagrams of dynamic models EMC for estimation temperatures

Figure 1.1 – Block diagrams of dynamic models EMC for estimation temperatures

At absence of the information on parameters WF or in integrated technical and economic calculations when factors, are known only, the dynamic model mass electric receiver strikes root in the form of, shown on fig. 1.1. Here on a link 4 inertial process w2T(t) after square-law inertial smoothing of factors of asymmetry acts.

Generally the group is connected to a network electric receiver with different constants of time of heating. It dynamic models will differ from each other in size parameter Т block SIS.

Average losses of capacity according to are calculated on a square of effective current of return sequence. For reception of this size after squarer 1 the link of 6 definitions of average value (fig. 1.2a) is provided. In a proportional link 4 multiplication to factor is made.

Block diagrams of dynamic models EMC for definition of average temperature, losses of the electric power and frequency rate of decrease in service life

Figure 1.2 – Block diagrams of dynamic models EMC for definition of average temperature, losses of the electric power and frequency rate of decrease in service life

Average value of losses of capacity according to proportional to a square of effective value of factor of asymmetry, therefore

The appropriating dynamic model is presented on fig. 1.2б. In it the link 4 has factor of transfer. Similar models for estimation average temperature differ only in factors of transfer of proportional links. The average temperature is parameter EMC for electric receivers with very big thermal inertia. Generally after it frequency rate of decrease in service life is defined. For this purpose in models on fig. 1.2 the proportional link 4 with factor of transfer b and exponential a link 5 is provided.

Inertial square-law smoothing

Progress of theory EMC began with normalization of parameters of quality of the voltage, concerning to a barrier x(t). Thus it was not considered, that the same barrier influences different electric receivers on a miscellaneous.

In [4] the principle of modeling of objects according to which the assessment of quality of the electric power was offered to be made not under characteristics of a barrier x (t), and under characteristics of reaction y (t) object on a barrier is stated. For this objective it is necessary to model considered object.

By analogy to [5] block WF (fig. 2.1), modeling reaction, we shall name the weighing filter. Squarer 1 considers that circumstance that influence of a barrier depends on capacity of reaction. Sluggishness object it is modeled by an inertial link 2 on which output square-law inertial process. proceeds. On an output of model block ПЭ of calculation of parameter EMC is stipulated.

Model of influence of a barrier

Figure 2.1 – Model of influence of a barrier

If the barrier changes slowly or sluggishness object is small, transients in blocks of model can be neglected. In this case reaction and a barrier are connected by functional dependence which is the static characteristic of object. Accordingly and model EMC will be static. Links 1 and 2 form block SIS of square-law inertial smoothing (squaring and smoothing). This block arbitrarily was called power. Models ЕМС should reflect the basic properties of objects, but to be maximum simple. Sluggishness object it is often enough to model an inertial link of the first order, the constant of time Т which coincides from constant inertia of object. In this case processes on an input and an output of block SIS are connected by the differential equation

Having designated through LT the operator of inertial smoothing, we shall record in a compact type

Square-law inertial process WT(t) has dimensionality of a square of reaction. In this connection it is convenient to use the resulted inertial process

which dimensionality of ordinates coincides with dimensionality of ordinates of reaction.

At square-law inertial smoothing on an input of a link moves y2 (t). If the initial chart is step, the formula for square-law inertial smoothing.

The chart of inertial process is under construction a method of consecutive intervals. If entrance process is set in the form of trellised function within the limits of each step of digitization there is no indispensability in construction of the chart of inertial process enough to calculate only final ordinates.

For periodic charts at once there is a stationary decision. After squarer the chart keeps the form, but sizes of steps are squared.

The chart of inertia process

Figure 2.2 – The chart of inertia process

Let's find in the beginning the greatest the least ordinates of square-law inertial process. For this purpose we shall record expressions:

having designated through:

having substituted absciss the ends of sites, we shall receive formulas for final ordinates

Here we shall add boundary conditions

Solving system of the algebraic equations, we shall receive:

After definition of these ordinates the chart of square-law inertial process in steady state (fig. 2.2) is under construction.

Calculation correlation functions under formulas of a type

It is complicated by that correlation function of entrance process contains absolute values of argument. As a result it is necessary to distinguish areas. Transformation of axes of coordinates receives formulas:

In the some people the variable of integration is positive. After integration the size is replaced on modul. In case of transformation under Кх, and correlation function and the standard of reaction WF also are understood as target process inertial process. At transformation

Under Кх correlation function of a square of reaction, and the day off is square-law inertial process. Averaging is carried out in following sequence, all over again the initial chart is squared (fig.2.3 curve 1), then the interval of averaging moves to the right on the step, the received cumulative process, is presented in picture of a curve 2. Taking from this chart a square root, we shall receive required process (a curve 3).

The cumulative chart of factors of asymmetry of a voltage at work ASMF-100

Figure 2.3 – The cumulative chart of factors of asymmetry of a voltage at work ASMF-100

Imitating modelling

Program StaSim which dialogue window is represented in picture 3.1 has been developed for modeling stationary accidental processes by student Evgeniej E.Ivko. In this program the modified method of statistical modeling of accidental processes, namely with an accidental choice of pairs rearranged ordinates as time of modeling in this case is less [6] is realized.

The window of the program

Рисунок 3.1 – The window of the program StaSim

The dialogue window of the program is divided into 6 blocks. In the block Цель имитации is defined objective of use of the program – modeling of new accidental process or improvement of quality of modeling (on correlation function) already existing process.

If as objective modeling new accidental process is chosen, it is necessary to pay attention to the block Моделирование нового случайного процесса. In it is necessary to set a population mean and the standard of received process, as well as a method of formation of sequence properly the distributed random variables.

Results of work of the program are brought in a file, namely the received accidental process, its correlation function (CF), the received maximal error of display CF concerning dispersion.

Regardless of the fact that it is chosen as objective of use of the program, it is necessary to set parameters of accidental process in the block Параметры случайного процесса: quantity of points, an interval of time between them and number of signs after a comma (is available I shall enter a format of a conclusion of data).

In the block Вид и параметры заданной КФ should be set a type and parameters reference CF to which will aspire statistical CF. Form СF maybe exponential, cosinusoil, exponential-cisinusoil or exponential-cosines-sinus.

Last block Корректирование КФ случайного процесса concerns process of approximation initial КФ to reference. In it the number points, which controlled CF, number of stages of improvement of quality of reconstruction КФ and sizes of the maximum allowable errors of reconstruction CF concerning dispersion on each of them is underlined. It is possible to specify at once some stages (then transition to a following stage will be automatically carried out and in a file of result it will be deduced only final results) or to specify quantity of stages equal to unit and at each following stage from them manually to correct value of the maximal error, it significantly accelerates process of updating CF and provides the way to trace variations.

The step of variation of a the maximum allowable error varies depending on parameters of accidental process, a type and parameters reference CF and quantities of controllable points. Nevertheless, especially at the first stage it is recommended to specify in advance well-off error (for example 1,5 relative units).

At successful work of the program there is an information window on which the actual maximal error (fig.3.2) is specified.

Result of work of the program

Figure 3.2 – Result of work of the program

Also it is necessary to note, that generation of new accidental process takes plenty of time, therefore for simplification of the further work of the program have been received, so-called, reference target processes with the parameters, specified in the program by default.

Reference

  1. ГОСТ 13109-97. Межгосударственный стандарт. Электрическая энергия. Электромагнитная совместимость технических средств. Нормы качества электрической энергии в системах электроснабжения общего назначения. – Введ. в Украине с 01.01.2000.
  2. Лютий О. П. Методи оцінювання параметрів несиметрії і несинусоїдальності режимів у системах електропостачання з різкозмінним навантаженням: Автореферат дис. канд. наук.: 05.14.12. – К.: 2003. – 19 с.
  3. Кузнецов В.Г., Куренный Э.Г., Лютый А.П. Электромагнитная совместимость. Несимметрия и несинусоидальность напряжения. – Донецк: «Норд-пресс», 2005.
  4. Куренный Э.Г., Ковальчук В.М., Коломытцев А.Д. Оценка качества электроэнергии с использованием моделей объектов. – В кн.: Качество электроэнергии в сетях пром. предприятий. Материалы конференции. – М.: МДНТП, 1977. – С. 23-29.
  5. CEI/IEC 61000-4-15. Electromagnetic compatibility – Part 4, Section 15: Flickermeter – Functional and design specification. 1997.
  6. Страница Магистра Ивко Е. Е. [Электронный ресурс]. – Режим доступа: http://masters.donntu.ru/2010/etf/ivko/library/article1.htm.
  7. Диссертация Погребняк Н. Н. «Методы квадратичного интерционного сглаживания в расчетах нагрузок промышленных электрических сетей» – Донецк, 1999. – 209 с.
  8. Страница Магистра Грузин С. А. [Электронный ресурс]. – Режим доступа: http://masters.donntu.ru/2009/eltf/gruzin/diss/index.htm.
  9. Шидловский А.К., Кузнецов В.Г. Повышение качества энергии в электрических сетях. – Киев: Наукова думка, 1985. – 268 с.
  10. Статья Куренный Э.Г., Дмитриева Е.Н. «Статистическое моделирование нормальных процессов в заводских электрических сетях», Академия наук СССР, 1977.
  11. Прохоров С.А. Математическое описание и моделирование случайных процессов. – Самар. гос. аэрокосм. ун-т, 2001. – 209 с.

At a writing of the given author's abstract master’s work is not completed. The final version of work can be received at the author or the supervisor of studies after December, 2012.