лабораторная работа / мэмс / 7lw

Ministry of science and education, youth and sport of Ukraine

Zaporozhie National Technical University

Department EEA

Report

Laboratory work#7

Done L.A.Askerova

Checked T.M.Kornus

Zaporozhie

2012

TOPIC: Modeling of steady state processes in nonlinear electric circuits of direct current by numerical method at MATLAB environment. Part 2.

PURPOSE OF THE WORK: Problem statement, development of the program of calculation of electrical state in the nonlinear circuit of a direct current by the Newton method using discrete current models._

Mathematical model

Let’s consider the example of the mathematical model development of the electric processes in the circuit represented in the figure 7.1 and analyze of them at MATLAB environment.

Figure 7.1 – Given electrical circuit

Let parameters values of elements are given as:

EMF – E1= 40 V; E2= 7 V;

Linear resistances – R1=5Ohm; R2=5 Ohm;

Nonlinear resistance Rn is given analytically accord to VACH:

I=5.5[lnU-1];

I’_f(U)=5.5/U;

.

Calculation of currents of the linear circuit shown in fig. 7.2 is carried out by the method of two nodes:

where J and G are parameters of discrete current model.

Then currents of branches are calculated accord to formulas

Figure 7.2 – The equivalent electrical circuit

The Block-diagram

Program that executes the task

%7lw

clear

clc

R1=5;

R2=5;

E1=40;

E2=7;

N=10;

%zero approach

I0=3;

%Initial approximation

I(2,1)=I0;

M=[1 1;

R1 -R2];

F=[I0;33];

i=M\F;

I(1,1)=i(1);

I(3,1)=i(2);

t(1)=1;

Ui(1)=0;

Ii(1)=5.5*(reallog(Ui(1))-1);

for k=2:0.5*N

U=exp(1+(I(2,k-1))/5.5);

G=5.5*1/U;

J=I(2,k-1)-U*G;

phi1=(E1/R1+E2/R2-J)/(1/R1+1/R2+G);

I(2,k)=J+phi1*G;

I(1,k)=(E1-phi1)/R1;

I(3,k)=(E2-phi1)/R2;

t(k)=k;

end

for k=2:4.1*N

%current curve

Ui(k)=Ui(k-1)+0.1;

Ii(k)=5.5*(reallog(Ui(k))-1);

end

%voltage curve

Iii=-15;

Uii(1)=0.1;

for n=2:3.5*N;

Iii(n)=Iii(n-1)+0.5;

Uii(n)=exp(((Iii(n))/5.5)+1);

end;

subplot(3,1,1),plot (t,I(1,t),t,I(2,t),t,I(3,t));

grid on

title ('Approaching of the currents in all branches')

xlabel('iterations');

ylabel('Currents');

legend('I1','I2','I3',-1)

subplot(3,1,2), plot(Ui,Ii);

grid on;title ('Current')

xlabel('voltage');

ylabel('current');

legend('I',-1);

subplot(3,1,3),

plot(Iii,Uii);grid on;

title ('Voltage')

xlabel('current');

ylabel('voltage');legend('U',-1);

Results of calculation

Graphical dependences of calculated currents through the branches of the given circuit (fig. 7.1.) accord to the every iteration step is represented in the figure 7.3.

The schedule of dependences of branches currents from number of iterations shows confident convergence of a method.

Figure 7.3 – Graphical dependences of calculated currents through the branches

The currents are:

I₁=6.3512A;

I₂=6.1023A;

I₃=-0.2488A.

Conclusion: The currents via varistor and branches were found. The graph of VAD is presented. The graph of differential is absent as there is no complicate sign in the given function.