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Amount of electro-receivers with a nonlinear voltage-current characteristic increases. Television sets, computers, energysaving lamps and other electro-receivers worsen electromagnetic compatibility (EMC). As a result, the losses of electric energy are unjustified magnified, an electrical equipment deteriorates, the control system work falsely, in a number of cases the health of people gets worse and diminishes the labour productivity. Expenses on overcoming of this problem are substantially higher than expenses on prevention.
Practical actuality of this master's work is providing of authenticity of the estimation of EMС not only on the stage of designing but also during exploitation of electric network.
Statistical modeling (imitation) of processes in the systems of power supply allows solving nonlinear problems which have no analytical decision. Imitation of characteristics of entrance hindrance with high exactness is necessary for determination of parameters EMC. A normal density of distribution and exponential correlation function are known.
Now for casual hindrances there are only approximate methods of the estimation EMC. The density distribution is calculated under on these approximate formulas, very strongly differs from normal and in places accepts negative values. But it contradicts physics become the distribution density cannot be subzero.
Scientific actuality of work is conditioned absence of analytical decision of tasks of estimation EMC for casual hindrances. The method of elementary processes is used in master's work for the decision of this task.
The purpose of work is research of authenticity the generation of the pseudo-random numbers, and also casual functions of time on the method of elementary processes.
The basic idea of work is the using of imitation of casual process that in fact replaces real experience.
Scientific novelty of work: dependences of extremums of inertia processes will be got on permanent inertia.
The scientific importance of work consists in development of theory EMC in area of determination of parameters of processes after the quadratic inertial smoothing.
The practical importance of work consists in objective estimation EMC on the additional overheat of electrical equipment and fatigue of people.
It is generated an array in the size N pseudo-random numbers of inferiors the exponential law of distribution
where λ=2/tц – intensity (average frequency) of appearance impulses, с-1,
tц = 1 – mean time of cycle, с.
Quality of imitation of casual electric processes is estimated by a method of confidential intervals under in advance known characteristics, namely on function of distribution and correlation function.
The scopes of confidence intervals are determined on probability of Eз n= 1 - Eз/n and degrees of freedom k=N-1, where N – an amount of experiments,Eз - set significance level. To these parameters with a table 3 and 4 [9] are found values βсn и εαn, that gives
Scopes of confidence interval for the coefficient of correlation at N≥25 determined [9]
Quality of imitation is considered comprehensible if statistical function to be in the middle of confidential area.
The confidential area for correlation function is defined with using borders of two parameters: the dispersion and correlation factor. At τ=0 [9] Rmin=Rmax=1, , therefore the boundary range on ordinate is limited Dmax и Dmin. At τ>0 borders are equal DmaxRmin and DmaxRmax. Theoretical correlation function should not overstep the bounds of area.
Idea realization is presented on fig. 1.
Figure 1 – Estimation of quality of imitation by the method of confidential intervals (the given image is animation with following parameters quantity of shots – 8; quantity of cycles of repetition – 5; 48,6 kb)
Following problems are solved in work:
- Have got the random numbers with the exponential distribution;
- Checking up of correctness of imitation;
- Checking up of accuracy of reproduction of elementary process with an exponential correlation function is checked up;
- Simulating the sum of elementary processes, checking up the correlation function and normal distribution.
Quality of imitation of casual process was estimated on correlation function the method of confidence intervals.
Dependence of variations of a dispersion and coefficient of correlation from quantity N has been received. It is recommended to take N≥1000 and then variation will not go out confidence intervals.
It is planned to build the inertia smoothing out of quadratic summary graph. The construction of dependence of inertia maximums and minimums of the smoothing out of quadratic summary graph from the parameter of correlation function will be end-point of work. As variant it will be executed the verification of possibility of imitation exponentially-cosinusoidal correlation function.
Practical importance of work – it is possible to determine the indicators EMC from “ГОСТ 13109-97” at the design stage.