The MATLAB File by Akshit Jain .pdf on .

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Akshit Jain Enrollment Number- TEN2103001
LAB FILE
of
Modeling and Simulation using MATLAB-Simulink
(EEE665)
Electrical Engineering Department
Faculty of Engineering, TMU
Jan 2024-May 2024
Submitted To: Submitted By: Akshit Jain
Mr. Umesh Kumar Singh (TEN2103001)
(Assistant Professor)

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INDEX
S.No. Name of Experiment Page
No.
Remarks Signature
1. Study of Introduction to MATLAB. 3
2. Single phase uncontrolled converter for R and RL
load with capacitor filter using MATLAB/SIMULINK.
6
3. Single Phase Fully Controlled Converter Using R and
RL Load Using MATLAB/SIMULINK.
9
4. Three Phase Fully Controlled Converter Using R and
RL Load Using MATLAB/SIMULINK.
12
5. Single Phase uncontrolled inverter using
MATLAB/SIMULINK.
15
6. Three Phase-Controlled Inverters by PWM
Technique Using MATLAB/SIMULINK.
16
7. Single phase AC voltage controller using
MATLAB/SIMULINK.
19
8. Study of Basic Matrix Operations Using
MATLAB/SIMULINK.
27
9. Determination of Eigen Values and Eigen Vectors of
a Square Matrix Using MATLAB Software.
30
10. To Solve Linear Equation Using MATLAB Software. 32
11. Determination of Roots of a Polynomial Using
MATLAB.
33
12. Solution of Difference Equations using MATLAB
Software
34

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 Starting MATLAB
Experiment: 01
Study of Introduction to MATLAB
After logging into our account, we can enter MATLAB by double-clicking on the MATLAB shortcut
icon (MATLAB 7.0.4) on your Windows desktop. When we start MATLAB, a special window called
the MATLAB desktop appears. The desktop is a window that contains other windows. The major
tools within or accessible from the desktop are:
•The Command Window
•The Command History
•The Workspace
•The Current Directory
•The Help Browser
•The Start button
1. Using MATLAB as a calculator: -
We will have noticed that if we do not specify an output variable, MATLAB uses a default variable
ans, short for answer, to store the results of the current calculation. Note that the variable ans is
created (or overwritten, if it is already existed). To avoid this, we may assign a value to a variable or
output argument name. For example:
X=12+1*2
X = 14
2. Creating simple plots: -
We need to prepare x and y in an identical array form; namely, x and y are row or column arrays of
the same length
The MATLAB command to plot a graph is plot (x, y).
>> x = [1 2 3 4 5 6];
>> y = [3 -1 2 4 5 1];
>> plot (x, y)

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By- Akshit Jain Enrol.no. – TEN2103001
3. Matrix generation: -
A vector is a special case of a matrix. The purpose of this section is to show how to create
vectors and matrices in MATLAB. As discussed earlier, an array of dimension 1 ×n is called
a row vector, whereas an array of dimension m × 1 is called a column vector. The elements
of vectors in MATLAB are enclosed by square brackets and are separated by spaces or by
commas.
3.1Entering matrix:-
To enter a matrix c c =
1 2 3
4 5 6
7 8 9
3.2Matrix functions: -
>> d
d =
1.0e+16 *
-0.4504 0.9007 -0.4504
0.9007 -1.8014 0.9007
-0.4504 0.9007 -0.4504
>> e
e =

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6.6613e-16
>> f
f =
1
5
9
>> g
g =
16.1168
-1.1168
-0.0000
>> h
h =
1.0e+16 *
-0.4504 0.9007 -0.4504
0.9007 -1.8014 0.9007
-0.4504 0.9007 -0.4504
>> i
i =
16.8481
>> j
j =
2
Introduction to programming in MATLAB
Commands with MATLAB is:
to create a file with a list of commands,
1. save the file, and
2. run the file.

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Experiment-02
Single phase uncontrolled converter for R and RL load with capacitor filter using
MATLAB/SIMULINK.
A diode rectifier or uncontrolled rectifier is the converter circuit that converts ac signal into (an
alternating signal) dc signal (unidirectional signal). Uncontrolled rectifier circuits use diodes to
convert ac power to dc power and are divided into two types, single-phase and three-phase.
Again singe-phase uncontrolled rectifiers are divided into two types, they are,
1. Half-wave uncontrolled rectifier
2. Full-wave uncontrolled rectifier
i. Center tapped rectifier
ii. Bridge rectifier
Single Phase Full Wave Bridge Rectifier with R-Load:
The below figure presents the circuit connection of a single-phase full-wave bridge rectifier loaded
with a resistive load. A full-wave bridge rectifier uses four diodes connected in a close-loop
configuration which converts alternating current into direct current. The ac input to the
uncontrolled full wave rectifier is given through a transformer.
Single Phase Full Wave Bridge Rectifier with R Load
When the ac supply source to the rectifier is turned ON, the positive half cycle of ac input starts.
During the positive half cycle of ac input, point A in the above circuit is made positive with respect
to point B. Due to this, diodes D1 and D2 are forward biased (since their anode terminals are
connected to positive with respect to the cathode), and diodes D3 and D4 are reverse biased (since
their anode terminals are connected to negative with respect to the cathode).

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Waveforms For Single Phase Full Wave Uncontrolled rectifier with R- Load
Thus, diodes D1 and D2 act as the closed switch and diodes D3 and D4 act as the open switch. Therefore, the
current starts flowing from point A, through diode D1, the load resistance R, and diode D2 to point B as shown
below in figure A. The load current will continue to flow through D1 and D2 until the positive half-cycle ends.
The average value of the load voltage Vdc can be calculated as follows,
Idc =2Vm/πR
The output dc power is given by,
Pdc = VdcIdc = 4Vm2/π2R
Single Phase Full Wave Bridge Rectifier with RL-Load:
In the above circuit, we have seen the full wave bridge rectifier with a resistive load where the output current and
voltage will be in phase. Let us see the circuit operation of an uncontrolled full wave bridge rectifier with RL-load.
The value of average output voltage and output current with RL

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Single Phase Full Wave Bridge Rectifier with RL Load
Waveforms for Single Phase Full Wave Uncontrolled Rectifier With RL

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Experiment- 03
Single Phase Fully Controlled converter using R and RL load using
MATLAB/SIMULINK
A single-phase bridge converter needs 4 thyristors. This configuration leads to two quadrant
operation. Such a converter is called the two-quadrant converter or fully controlled converter. Many
times, the bridge circuit is modified by replacing two thyristors by two diodes. This configuration
leads to one quadrant operation (operation is restricted to first quadrant). Such a converter is called
the one-quadrant converter or a semi converter.
The load on the converter may be purely resistive, inductive (R-L) load or R-L-E load. An R-L-E load
consists of resistance, inductance and motor (E stands for back emf of motor). The load may also
have a battery (emf E) instead of motor.
Single phase fully controlled rectifier using R Load
1. With Resistive Load: A fully controlled full-wave bridge rectifier is shown in Fig. All the four
devices used in the circuit are thyristors TH1-TH4 for control of output power. In this
circuit, diagonally opposite pair of thyristors are made to conduct, and are commutated,
simultaneously. During the first positive half cycle, thyristors TH1 and TH3 are forward
biased and if they are triggered simultaneously, the current flows through the load via
thyristor TH1-load-TH3-source. Thus, during positive half cycle, thyristors TH1 and TH3 are
conducting. During the negative half cycle of the ac input, thyristors TH2 and TH4 are
forward biased andif they are triggered simultaneously, the current flows through the load
via thyristor TH2- load-TH4-source. Thyristors TH1, TH3 and TH2, TH4 are triggered at the
same firing angle α in each positive and negative half cycles of the supply voltage
respectively. When the supply voltage falls to zero, the current also becomes zero. Thus,
thyristors TH1, TH3 in positive half cycle and TH2 and TH4 in negative half cycle turn off by
natural commutation.

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Voltage and Current waveforms ofcircuit are Depicted
Single Phase Fully Controlled Rectifier With R-L Load
The voltage waveform at the dc terminals comprises a steady dc component superimposed with
an ac ripple component, having a fundamental frequency equal to twice that of ac supply.

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Single Phase Fully Controlled Rectifier with RL Load
The average output dc voltage is given b
The average value of output dc voltage can be varied, by varying firing angle α, continuously from
positive maximum to negative maximum, assuming continuous current flow at the dc terminals.
Because the average dc voltage is reversible even though the current flow in the load is
unidirectional, the power flow in the convener can be in either direction.

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Experiment-04
Three Phase Fully Controlled Converter Using R and RL Load
Using MATLAB/SIMULINK
A three-phase full-wave controlled rectifier, also known as a three-phase thyristor rectifier or six-
pulse rectifier, is a type of rectifier circuit used to convert alternating current (AC) into direct current
(DC). It utilizes six thyristors (also known as silicon-controlled rectifiers or SCR) to control the flow
of current. Here's how a three-phase controlled rectifier works:
1. Kirchhoff’s voltage law around any path shows that only one thyristor in the top half of the bridge
may conduct at one time (S1, S3, or S5). The thyristor that is conducting will have its anode connected
to the phase voltage that is highest at that instant.
2. Kirchhoff’s voltage law also shows that only one thyristor in the bottom half of the bridge may
conduct at one time (S2, S4, or S6). The thyristor that is conducting will have its cathodeconnected to
the phase voltage that is lowest at that instant.
3. As a consequence of points 1 and 2, S1 and S4 cannot conduct at the same time. Similarly,S3 and S6
cannot conduct simultaneously, nor can S5 and S2.
4. The output voltage across the load is one of the line-to-line voltages of the source. For example,
when S1 and S2 are on, the output voltage is Vac. Furthermore, the thyristors that are on are
determined by which line-to-line voltage is the highest at that instant. For example, when Vac is the
highest line-to-line voltage, the output is Vac.
Three Phase Full Wave Controlled Rectifier R Load
Single Phase AC Voltage Controller

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Waveforms of Three Phase Full Wave SCR with R Load
One thyristor of the conducting pair powers the positive side of load, while the other thyristor
powers the negative side of the load. Thyristors T1, T3, T2, and T4 form a bridge rectifier network
between phases A and B, similary thyristors T3, T5, T4, and T6 between phases B and C and T5, T1, T6,
Three Phase Full Wave Controlled Rectifier - RL Load
Three Phase Full Wave SCR with RL Load

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Waveforms of Three Phase Full Wave SCR with RL Load

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Experiment-05
Single Phase uncontrolled inverter using MATLAB/SIMULINK
A single-phase voltage source inverter inverts the DC voltage into square-wave ac or sine-wave ac
voltages. Currently, there are two types of voltage inverters on the market: the first is a full-bridge
voltage source inverter, which consists of four switches, IGBTs, or MOSFETs, and the second is a
single-phase voltage source inverter, which consists of two switches, IGBTs, or MOSFETs. These
voltage source inverter applications include single phase UPS and switching power supplies. These
have been mostly used in high-power static power topologies.
Simulink Model of Single-Phase Voltage Source Inverter
In this article, we will explain how we can make a single-phase voltage source inverter as well as
how we choose the components with the help of the MATLAB Simulink model. First, we will explain
how we can make a new model in MATLAB. To make a new model, just open MATLAB and click on
the Simulink library. After clicking on Simulink Library, a new page will open with the name Simulink
Library Browser.
Simulink Model
Similarly, we search and drag all the other component blocks, such as the pulse generator, logic
gate, capacitor, resistor, etc. Then we join the circuit according to our requirements. Now our single-
p
h
a
s
evoltage source inverter is complete with the help of the MATLAB Simulink library. The Simulink
model circuit can be seen in the figure below.
Simulation
Because both IGBT switches should not be ON at the same time, one gate pulse directly connects
with one IGBT switch, and the other gate pulse is connecting with the other IGBT switch after NOT
Gate. In other words, this circuit works through complementary switching. When we simulate this
circuit at 50% duty cycle, then the output voltage would be half of the supply voltage, which means
it would be 50 volts, as shown in the figure below.

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Experiment-06
Three Phase-Controlled Inverters by PWM Technique Using
MATLAB/SIMULINK
In electrical engineering, inverters are one of the basic circuits used and are mostly used in UPS
(uninterrupted power supply), which is present in almost every house now. Hence, the basic
purpose of an inverter is to convert direct current (DC) to alternating current (AC), which is no doubt
the opposite of rectifiers. So, for beginners, the definition of AC voltage can be taken as the voltage
that changes its direction from positive voltage to negative voltage across the same terminal in a
specified period of time over and over again. A simple sinusoidal wave is an AC wave. However, DC
can be defined as a constant source of voltage that remains either positive or negative over time.
Design Three Phase Inverter Using Simulink MATLAB
Open MATLAB and then open Simulink using the Simulink icon on MATLAB, as we have been doing
in previous tutorials. Create a new blank model and save it in the first hand so we can access it in
the future. Now, click on the library browser icon on Simulink’s recently created model. In the library
browser, select the section named “Simscape”, as shown in the figure below.
Three Phase Bridge
Place six such diodes on the model we created previously and arrange them in three rows with two
thyristors each. Connect all of them to make a bridge, as shown in the figure below.
Load and Source
At the input side of the bridge, we created previously, connect the DC voltage source, and at the
output, connect the load (change the RLC load to only a resistive load) with each branch to each row
as shown in the figure below.

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As the phase delay is in seconds, the phase delay of the second pulse generator will be (2e-3)
*(1/6),and so on. All six pulse generators connected are shown in the figure below.

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Simulink Model
At the output, connect the voltage measurement across each resistor and connect the scope at the
output of each voltmeter, as shown in the figure below.

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Experiment 07
Single phase AC voltage controller using MATLAB/SIMULINK
The ac voltage controller also called as AC Regulator is a static power electronic circuit that converts
fixed ac to variable ac. It accomplishes this task without a change in frequency. It finds application
in heating, lighting circuits, speed control of ac machines, fan regulators, etc., similar to the
applications of an autotransformer.
The circuit of the ac voltage controller is based on either thyristor, TRIACs, SCRs, or IGBTs, which
gives a variable ac at the output when their triggering angle is adjusted or varied. The output voltage
is either increased, decreased, or kept constant by varying the RMS value of input fixed alternating
voltage.
Classification of AC Voltage Controllers:
Depending upon the supply, ac voltage controllers are divided into two types. They are,
 Single-phase ac voltage controller
 Half-wave voltage control or unidirectional ac voltage controller
 Full-wave control or bidirectional ac voltage controller
 Three-phase ac voltage controller
 Half-wave voltage control or unidirectional ac voltage controller
 Full-wave control or bidirectional ac voltage controller
Single Phase Half Wave AC Voltage Controller:
The below shows the single-phase half-wave or unidirectional ac voltage controller circuit
with output voltage and current waveforms.
Single-phase half-wave ac voltage controller consists of one thyristor in anti-parallel with one diode.
The power delivered to the load will depend upon the firing angle of the thyristor. During the
positive half cycle of supply voltage, only the thyristor is forward-biased. The thyristor will conduct
from α to π.
At ωt = π, the thyristor will get turn-off for R-load. Now, when the negative half cycle starts diode
will get forward biased (i.e., from π to 2π) and it conducts. Only the positive half cycle is controlled
in a single-phase half-wave ac voltage controller due to this reason it is also known as a
unidirectional ac voltage controller. The average value of the output voltage is given by,

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Unidirectional ac voltage controllers are only suitable for low-power resistive loads like heating and
lighting.
Single Phase Full Wave AC Voltage Controller:
The full-wave or bidirectional ac voltage controller uses two thyristors instead of one thyristor and
diode. The two thyristors are connected in anti-parallel. Let see the working of full-wave ac voltage
controller with resistive (R) load and resistive-inductive (RL) load.
Single Phase Full Wave AC Voltage Controller with ResistiveLoad:
The power circuit diagram for a single-phase ac voltage controller with a resistive load is shown in
the below figure. The power delivered to the load flows through thyristor T1 during the positive half-
cycle and through thyristor T2 during the negative half-cycle.
Single Phase AC Voltage Controller Using Resistive Load
During the positive half cycle of the source voltage VS, SCR T1 is forward biased and SCR T2 is reverse
biased. No conduction of load current takes place until thyristor T1 is triggered at some firing angle
α. So, the entire supply voltage VS appears across thyristor T1 with the same polarity and across T2
with the reversed polarity. As soon as the thyristor T1 is triggered at the instant ωt = α, T1 starts
conducting and the entire supply voltage VS, except the drop across T1, appears across the load
resistance.

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W
a
v
e
f
o
r
m
s
S
Single-phase AC Voltage Controller Using R- Load
The above shows the waveforms for source voltage, gating signals, output voltage, output current,
and the voltage across the SCRs. At ωt = π, the load voltage, the load current falls to zero and
therefore T1 stops conducting. Thereafter thyristor T2 will be forward biased and T1 will be
reversebiased and of course, there will be no conduction until T2 is triggered i.e., until (π + α).

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As long as thyristor T1 in ON state, i.e., from α < ωt < π, voltage across T2 will be VT2 = – VT1 = -
(ON- state voltage drop of T1). At ωt = (π + α), thyristor T2 is triggered and it starts conducting.
Except for the small voltage drop across T2, the entire supply voltage appears across the load
resistance and the load current flows. As long as T2 is in ON state, i.e., from (π + α) < ωt < 2π,
voltage across T1 willbe VT1 = -VT2 = -(ON-state voltage drop of T2).
This process goes on and continues for every cycle as shown in the waveform. For resistance load,
the source current waveform will follow the source voltage waveform i.e., both the voltage and
current of the source will be in phase with each other.
If the firing angles at which the thyristors T1 and T2 are same. The RMS value of output voltage and
current with resistive load is given by,
Single Phase Full Wave AC Voltage Controller with RL Load
The below shows the single-phase ac voltage controller circuit with resistive and inductive load.

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Single Phase AC Voltage Controller
Operation When α ≤ Φ:
Consider α = Φ (load phase angle) i.e., the ac voltage regulator is operating under steady-state
conditions. The conduction period of SCR T2 is from zero to Φ and from Φ to (π + Φ) SCR T1 will
conduct and again from (π + Φ) to (2π + Φ) SCR T2 will conduct as shown in the waveform below.
Waveforms for Single Phase AC Voltage ontrolled with RL Load

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Waveforms for single phase AC Voltage controlled with RL Load
Thus, from Φ to (π + Φ), T1 will conduct. If T2 is triggered at a firing angle (π + α) < (π + Φ), then
T2 will remain OFF because T1 is conducting a current iT1 and the voltage drop across T1 will make
SCR T2 reverse bias. At ωt = (π + Φ), T2 will get turned ON since the voltage drop and conduction
current in T1 at this instant becomes zero. Thus, SCR T2 will conduct from (π + Φ) to (2π + Φ).
At the instant ωt = π, the load and source voltages become zero but, the current possesses some
value due to the presence of inductance at the load side. So, thyristor T1 continues to conduct
until the current flowing through it becomes zero. The angle at which thyristor current becomes
zero is known as extinction angle β. So, output voltage and current are equal to source voltage and
current from α to β respectively.
From angle β to (π + α), the value of load voltage and load current will be zero. At the instant ωt =
(π + α), thyristor T2 is triggered and it starts conducting. So, the load current which is the same as
current iT2 through T2 will flow in the reverse direction.
At the end of the first cycle i.e., at the instant ωt = 2π source voltage VS and load voltage
VO becomes zero but the current doesn’t become zero. At the instant ωt = (π + α + γ) where, ωt = γ

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For High Inductance Value
It is known as conduction angle, the thyristor current iT2 becomes zero. This turns OFF thyristor
T2and it get reverse biased as shown in the waveform
.

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The RMS value of output voltage and current with RL load is given by,

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Experiment 08
Study of Basic Matrix Operations Using MATLAB/SIMULINK
The basic operations on Matrix are as follow:
Write a Matrix in MATLAB
A= [1 1 -2; 2 2 1; 2 1 1]
Find the size of a Matrix
The size of a Matrix is its number of rows and columns. To find the size of a Matrix, use the
following code
Size(A)
Add A and C using the following code
A+C
Divide Matrices element by element
To divide two Matrices element by element, use the following
A/C
Find the inverse of a Matrix
To find the inverse of a Matrix in MATLAB, use the following code
Inv(A)

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1. Find the determinant of a Matrix
To find the determinant of a Matrix in MATLAB, use the following code
Det(A)
2. Define a Matrix with Random elements
To create a Matrix with Random element in Matlab, use
Rand (3,2)
3. Find the diagonal of a Matrix
To find the main diagonal of A, use
Diag(A)
4. Compute the Transpose of a Matrix
To find the transpose of a Matrix, use the following: -

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Matrix Multiplication

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Experiment 09
Determination of Eigen Values and Eigen Vectors of a Square Matrix Using MATLAB
Software
Eigen values and Eigen vectors are properties of a square matrix.
Let is an N*N matrix, X be a vector of size N*1 and be a scalar.
Then the values X, satisfying the equation are eigenvectors and eigenvalues of matrix A
respectively.
o A matrix of size N*N possess N eigenvalues
o Every eigenvalue corresponds to an eigenvector.
Matlab allows the users to find eigenvalues and eigenvectors of matrix using eig() method.
Different syntaxes of eig() method are:
o e = eig(A)
o [V,D] = eig(A)
o [V,D,W] = eig(A)
o e = eig(A,B)
Let
e = eig(A)
• It returns the vector of eigenvalues of square matrix A.

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Output:
[V, D] = eig(A)
o It returns the diagonal matrix D having diagonals as eigenvalues.
o It also returns the matrix of right vectors as V.
o Normal eigenvectors are termed as right eigenvectors.
o V is a collection of N eigenvectors of each N*1 size (A is N*N size) that satisfies A*V
= V*D
% Square matrix of size 3*3
Output:

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Experiment 10
To Solve Linear Equation Using MATLAB Software
We can use the MATLAB built-in function solve () to solve the system of linear equations in MATLAB.
First of all, we can define the variables using the syms variable. After that, we can write the
equations in MATLAB. After that, we need to use the function solve () to solve the equations. For
example, let’s define some equations in MATLAB and find their solution using the solve () function.
See the code below.
Output:
The function linsolve() is used instead of the solve() function if you have matrices instead of
equations. We can also convert the equations to matrix form using the equations To Matrix()
function. For example, let’s define some equations in Matlab and find their solution using the
linsolve() function. See the code below.

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Experiment 11
Determination of Roots of a Polynomial Using MATLAB
Syntax r = roots(p) returns the roots of the polynomial represented by p as a column vector. Input
p is a vector containing n+1 polynomial coefficients, starting with the coefficient of xn
. For example,
p = [3 2 -2] represents the polynomial 3x2+2x−2. A coefficient of 0 indicates an intermediate power
that is not present in the equation.
The root’s function solves polynomial equations of the form p1xn+...+pnx+pn+1=0. Polynomial
equations contain a single variable with nonnegative exponents.
Examples
1. Roots of Quadratic Polynomial: -
 Use the poly function to obtain a polynomial from its roots: p = poly(r). The poly function
is the inverse of the roots function.
 Use the f zero function to find the roots of nonlinear equations. While the root’s function
works only with polynomials, the zero function is more broadly applicable to different
types of equations.
Roots of a Polynomial

Page | 34
Experiment 12
Solution of Difference Equations using MATLAB Software
First-Order Linear ODE
Solve this differential equation.
dy/dx=ty
Fiíst, represent y by using symsto create the symbolic function
y(t).symsy(t)
Define the equation using ==and represent diffeíentiation using the difffunction.
ode = diff (y, t) == t*y
ode(t) = diff(y(t), t) == t*y(t)
Solve the equation using dsolve.
ySol(t) = dsolve(ode)
ySol(t)= C1*exp(t^2/2)
Solve Differential Equation with Condition
In the previous solution, the constant C1appears because no condition was specified. Solve the
equation with the initial condition y(0) == 2. the dsolvefunction finds a value of C1that satisfies the
condition.
cond = y(0) == 2;
ySol(t) = dsolve(ode,cond)
ySol(t) =2*exp(t^2/2)
.
Nonlinear Differential Equation with Initial Condition: -Solve this nonlinear differential
equation with an initialcondition. the equation has multiple solutions.
Second-Oídeí ODE with Initial Conditions
Solve this second-order differential equation with two initial conditions.

Page | 35
d2
y/dx2
=cos(2x)-y
y (0)=1
y’
(0)=0
Steps: -Define the equation and conditions. The second initial condition involves the first derivative
of y. Represent the derivative by creating the symbolic function Dy = diff(y) and thendefine the
condition using Dy (0) ==0.
syms y(x)
Dy = diff(y);
ode = diff(y,x,2) == cos(2*x)-y;cond1
= y(0) == 1;
cond2 = Dy(0) == 0;
Solve odefor y. Simplify the solution using the simplifyfunction.
conds = [cond1 cond2]; ySol(x)
= dsolve(ode,conds);ySol =
simplify(ySol)
ySol(x) = 1 - (8*sin(x/2)^4)/3

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