how to have a continious sine wave in different periods

hello guys,

I have created a code to generate a kind of three phases voltage drop, but i have a problem connecting between the curves in the different periods .. i dont have a problem in the first phase which its angle is 2*pi ... but in the 2 others phases where i have 2*pi/3 and -2*pi/3 i cant connect between them

[azerty and qwerty]

to be more clear i put my code and what i get and what i want to get :

clc;
clear all;
close all;

%% Declaration of initial variables
fs = 5000;                      % Sampling Frequency in Hz
t1 = linspace(0,1000,fs) ;       % Period in ms
f = 50;                         % Frequency in Hz
U1=230;                         % Supply voltage

FontSize = 10;

%% For VOLTAGE

MyVoltage1 = U1*sin(2*pi*f*t1);         % Sine wave generation
MyVoltage2 = U1*sin(2*pi*f*t1+2*pi/3);
MyVoltage3 = U1*sin(2*pi*f*t1-2*pi/3);

subplot(5,1,1);
plot(t1,MyVoltage1, t1,MyVoltage2, t1,MyVoltage3)
grid on;

xlabel('My Voltage', 'FontSize', FontSize)
ylabel('Tension (V)', 'FontSize', FontSize)

title ('Generation of voltage dips of 70%', 'FontSize', FontSize);

%% Declaration of initial variables

fs = 5000;                     % Sampling Frequency in Hz
t2 = linspace(1000,1500,fs) ;   % Period in ms
f = 50;                        % Frequency in Hz
P=0.7;                         % disturbance percentage 
U2=230*P;                      % Perturbation

%% For PERTURBATION

MyPerturbation1 = U2*sin(2*pi*f*t2);         % Sine wave generation
MyPerturbation2 = U2*sin(2*pi*f*t2+2*pi/3);
MyPerturbation3 = U2*sin(2*pi*f*t2-2*pi/3);

subplot(5,1,2);
plot(t2,MyPerturbation1, t2,MyPerturbation2, t2,MyPerturbation3)
hold on
grid on;

xlabel('My Perturbation', 'FontSize', FontSize)
ylabel('Tension (V)', 'FontSize', FontSize)

%% For VOLTAGE DIPS

%signal = MyVoltage+MyPerturbation;           % Voltage dips generation

subplot(5,1,3);
plot(t1,MyVoltage1,'r', t1,MyVoltage2,'r', t1,MyVoltage3,'r' , t2, MyPerturbation1,'b', t2, MyPerturbation2,'b', t2, MyPerturbation3,'b')
grid on;

xlabel( 'My Voltage Dip', 'FontSize', FontSize)
ylabel('Voltage (V)', 'FontSize', FontSize)

%% Declaration of initial variables
fs = 5000;                      % Sampling Frequency in Hz
t3 = linspace(1500,2500,fs) ;   % Period in ms
f = 50;                         % Frequency in Hz
U1=230;                         % Supply voltage

FontSize = 10;

%% For VOLTAGE
%MyPerturbation1 = U2*sin(2*pi*f*t2)

MyVoltage1 = U1*sin(2*pi*f*t3);         % Sine wave generation
MyVoltage2 = U1*sin(2*pi*f*t3+2*pi/3);
MyVoltage3 = U1*sin(2*pi*f*t3-2*pi/3);

subplot(5,1,4);
plot(t3,MyVoltage1, t3,MyVoltage2, t3,MyVoltage3)
grid on;

xlabel('My Voltage', 'FontSize', FontSize)
ylabel('Tension (V)', 'FontSize', FontSize)

%% For FINAL VOLTAGE DIPS

%signal = MyVoltage+MyPerturbation;      % Voltage dips generation

subplot(5,1,5);
plot(t1,MyVoltage1,'r',t1,MyVoltage2,'r',t1,MyVoltage3,'r', t2,MyPerturbation1,'b',t2,MyPerturbation2,'b',t2,MyPerturbation3,'b', t3,MyVoltage1,'g',t3,MyVoltage2,'g',t3,MyVoltage3,'g')
hold on
grid on;

xlabel( 'My Voltage Dip', 'FontSize', FontSize)
ylabel('Voltage (V)', 'FontSize', FontSize)

so thats the curves i get :

as u can see the other phases are not connected when i do my voltage drop ...

what i want to get is this :

[Sam Chak]

Hi @azerty and qwerty

These three waves have the same period, but different phases.

Please mark the intersection points where you want to connect them as a single discontinuous wave.

x = linspace(-pi, 2*pi, 1001)';
y1 = sin(x + 2*pi/3); 
y2 = sin(x + 2*pi); 
y3 = sin(x - 2*pi/3); 
y = [y1 y2 y3];
plot(x, y, 'linewidth', 1.5)

[azerty and qwerty]

its not working .. i tried to make a new sine wave and connect them before by creating a new sine wave but it doesnt help ... im searching if there is a function that relate 2 curves or something

[Sam Chak]

I see... Need to calculate the exact points where the two adjacent sine waves continuous.

[azerty and qwerty]

i tried using

plot(t1,MyVoltage1,'r', t1,MyVoltage2,'r', t1,MyVoltage3,'r', t2, MyPerturbation1+MyVoltage1(end),'b', t2, MyPerturbation2+MyVoltage2(end),'b', t2, MyPerturbation3+MyVoltage3(end),'b')

but its not working aswell

[Sam Chak]

By the way, how many cycles in between 0 and 1000 sec for a sine wave ?

t = linspace(0, 1000, 5000);
y1 = sin(2*pi*50*t);
y2 = sin(2*pi/100*t);
y = [y1' y2'];
plot(t, y)
legend('y1', 'y2')

Answer 1

[Sam Chak]

@azerty and qwerty

Think you probably want to show something like this.

Do you remember I mentioned about the points where there is a continuity when the voltages dip? I picked the points when V = 0.

fs = 10001;                         % Sampling Frequency in Hz
t1V1 = linspace(0, 0.30/3, fs);     % Period in ms
t1V2 = linspace(0,   7/75, fs);
t1V3 = linspace(0,   8/75, fs);

MyVoltage1 = U1*sin(2*pi*f*t1V1);           % Sine wave generation
MyVoltage2 = U1*sin(2*pi*f*t1V2 + 2*pi/3);
MyVoltage3 = U1*sin(2*pi*f*t1V3 - 2*pi/3);

t2V1 = linspace(0.30/3, 0.2, fs);  % Period in ms
t2V2 = linspace(  7/75, 0.2, fs);
t2V3 = linspace(  8/75, 0.2, fs);

MyPerturbation1 = U2*sin(2*pi*f*t2V1);      % Sine wave generation
MyPerturbation2 = U2*sin(2*pi*f*t2V2 + 2*pi/3);
MyPerturbation3 = U2*sin(2*pi*f*t2V3 - 2*pi/3);

plot(t1V1, MyVoltage1, 'r', t1V2, MyVoltage2, 'b', t1V3, MyVoltage3, 'g' , t2V1, MyPerturbation1, 'r', t2V2, MyPerturbation2, 'b', t2V3, MyPerturbation3,'g')

[azerty and qwerty]

i understand what u mean but when i need a specific period for ex from 0 to 1000 ms and if i want to change it from 0 to 500 ms .. i have to calculate the passage of 0 everytime .. there is no automatic way to do it ?

[Sam Chak]

Hi @azerty and qwerty

I'm not aware of any special function, but you can definitely perform a little math and program it in the script as shown in the following example:

Solving gives

where .

Rearranging this yields

Similarly, solving and give

, and

, respectively.

tdipV1 = 500;       % desired time for voltage dip to occur
n = 100*tdipV1;
tdipV2 = 1/300*(3*n - 2);
tdipV3 = 1/300*(3*(n + 1) - 4);

tstart = tdipV1 - 0.03;
tfinal = tdipV1 + 0.03;
fs   = 10001;
t1V1 = linspace(tstart, tdipV1, fs);
t1V2 = linspace(tstart, tdipV2, fs);
t1V3 = linspace(tstart, tdipV3, fs);

f  = 50;
U1 = 230;
U2 = 0.7*U1;

MyVoltage1 = U1*sin(2*pi*f*t1V1);
MyVoltage2 = U1*sin(2*pi*f*t1V2 + 2*pi/3);
MyVoltage3 = U1*sin(2*pi*f*t1V3 - 2*pi/3);

t2V1 = linspace(tdipV1, tfinal, fs);
t2V2 = linspace(tdipV2, tfinal, fs);
t2V3 = linspace(tdipV3, tfinal, fs);

MyPerturbation1 = U2*sin(2*pi*f*t2V1);
MyPerturbation2 = U2*sin(2*pi*f*t2V2 + 2*pi/3);
MyPerturbation3 = U2*sin(2*pi*f*t2V3 - 2*pi/3);

plot(t1V1, MyVoltage1, 'r', t1V2, MyVoltage2, 'b', t1V3, MyVoltage3, 'g' , t2V1, MyPerturbation1, 'r', t2V2, MyPerturbation2, 'b', t2V3, MyPerturbation3,'g')
grid on
xlabel('t')
ylabel('V')
title('Voltage Dip around 500 s');