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Single Phase Voltage Calculation | Matlab

Here, we will find phase voltages VAN, VBN, and VCN, shown in the following figure, using Matlab.

By applying KVL, we come up with the following three equations:

$\begin{matrix}   110\angle {{0}^{o}}=(1+j1){{I}_{1}}+(5+j12){{I}_{1}} & \cdots  & (1)  \\   110\angle -{{120}^{o}}=(1-j2){{I}_{2}}+(3+j4){{I}_{2}} & \cdots  & (2)  \\   110\angle {{120}^{o}}=(1-j0.5){{I}_{3}}+(5-j12){{I}_{3}} & \cdots  & (3)  \\\end{matrix}$

After simplifying above equations, we have

$\begin{matrix}   110\angle {{0}^{o}}=(6+j13){{I}_{1}} & \cdots  & (4)  \\   110\angle -{{120}^{o}}=(4+j2){{I}_{2}} & \cdots  & (5)  \\   110\angle {{120}^{o}}=(6-j12.5){{I}_{3}} & \cdots  & (6)  \\\end{matrix}$

Let’s put the above three equations in matrix form,

$\left[ \begin{matrix}   6+j13 & 0 & 0  \\   0 & 4+j2 & 0  \\   0 & 0 & 6-j12.5  \\\end{matrix} \right]\left[ \begin{matrix}   {{I}_{1}}  \\   {{I}_{2}}  \\   {{I}_{3}}  \\\end{matrix} \right]=\left[ \begin{matrix}   110\angle {{0}^{o}}  \\   110\angle -{{120}^{o}}  \\   110\angle {{120}^{o}}  \\\end{matrix} \right]$

Now, we can write the above matrix as:

\[\left[ Z \right]\left[ I \right]=\left[ V \right]\]

From above, we can easily calculate unknown currents using:

$I=inv(Z)*V$

And for the phase voltages:

\[\begin{matrix}   \begin{align}  & {{V}_{AN}}=(5+j12){{I}_{1}} \\ & {{V}_{BN}}=(3+j4){{I}_{2}} \\ & {{V}_{CN}}=(5-j12){{I}_{3}} \\\end{align} & \cdots  & (7)  \\\end{matrix}\]

Now, it’s time to write Matlab code to find out the phase voltages using the above formulas.

Measure phase voltages in three-phase system using Matlab


clear all;close all;clc
% Phase Voltages Calculation using Matlab
Z = [6-13*j 0 0;
0 4+2*j 0; % Z-Matrix (Impedance Matrix) from text
0 0 6-12.5*j];
c1=110; %Angle is 0 degree here so we simply ommit it
c2 = 110*exp(j*pi*(-120/180)); % Voltages expressed in phasor form (V=Vm*exp(j*theta))
c3 = 110*exp(j*pi*(120/180)); % Angles are converted into radians (=degrees*pi/180)
V = [c1; c2; c3]; % Voltage Vector [V] mentioned in the text
I = inv(Z)*V; % Calculate unknown Loop currents
%% Phase Voltages Calcualtion
V_an = (5+12*j)*I(1);
V_bn = (3+4*j)*I(2); % Calcualting Phase Voltages using equation (7) in text
V_cn = (5-12*j)*I(3);
% Magnitude and Angle Calculation for each Phase Voltage
V_an_abs = abs(V_an);
V_an_ang = angle(V_an)*180/pi;
V_bn_abs = abs(V_bn);
V_bn_ang = angle(V_bn)*180/pi;
V_cn_abs = abs(V_cn);
V_cn_ang = angle(V_cn)*180/pi;
%% Print out Results
fprintf('Phase Voltage Van \n Magnitude: %f \n Angle in degree: %f \n', V_an_abs, V_an_ang)
fprintf('Phase Voltage Vbn \n Magnitude: %f \n Angle in degree: %f \n', V_bn_abs, V_bn_ang)
fprintf('Phase Voltage Vcn \n Magnitude: %f \n Angle in degree: %f \n', V_cn_abs, V_cn_ang)

Results

Phase Voltage Van

 Magnitude: 99.875532

 Angle in degree: 132.604994

Phase Voltage Vbn

 Magnitude: 122.983739

 Angle in degree: -93.434949

Phase Voltage Vcn

 Magnitude: 103.134238

 Angle in degree: 116.978859

About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.

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