Power Converters Simulation Lab Manual-[2015-2016] 4cz25

Power Converters Simulation Lab Manual

List of Experiments:

1. Single phase fully controlled converter using RL & RLE loads. 2. Three phase full converter using RL & RLE loads. 3. Single phase AC voltage controller Using RL load. 4. Three phase Inverter with PWM Controller. 5. DC-DC converter. 6. Modeling of Separately excited DC motor. 7. Write a program and simulate dynamical system of following models. a) I/O Model. b) State variable Model. 8. Obtain frequency response of a given system by using various methods. a) General Method of finding frequency domain specifications. b) Polar Plot c) Bode plot. Also obtain Gain Margin & Phase Margin for the above. 9. Design a compensator for a given system for required specifications. 10. Develop a program to solve Swing Equation.

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :1

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

SINGLE PHASE FULL CONVERTER AIM:Simulate a single phase full converter with R,RL&RLE loads to find out theoutput voltageand extinction angle using MATLAB software.

CIRCUIT DIAGRAM:

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POWER CONVERTERS SIMULATION LAB (PG) THEORY AND OPERATION: Rectification is a process of converting an alternating voltage or current into a direct voltage or current.The fully controlled converter uses thyristors,as the rectifying elements and the dc output voltage is a function of supply voltage and firing angle of thyristors.With a fully controlled converter it is possible, by controllingthe firing angle, to allow power to be transferred from dc side of the rectifier back into the ac system.Therefore, fully controlled converter is referred to as bi-directional converter. OPERATION WITH RESISTIVE LOAD: During the first positive half cycle, SCR’s T1 and T4 are forward biased and if they are triggered simultaneously at an angle α, the current flows through the load.When the supply voltage falls to zero, current also goes to zero and hence T1 and T4turns off by natural commutation.During the negative half cycle, T2 and T3are forward biased and if they are triggered simultaneously, current flows through the load in the same direction as explained before. OPERATION WITH R-L LOAD: During the positive half cycle, when thyristor and thyristor1 are forward biased and if they are triggered simultaneously at an angle α, the current flows through the load.At instant π, voltagereverses, but the current is maintained in the same direction due to the presence of inductance,which keeps the SCR’s T1 and T4in conducting state, and hence the negative supply voltage will appear across the load till T2 and T3are triggered.During the negative half cycle, the SCR’s T2 and T3are forward biased and are triggered simultaneously at π+α and then current flows through the load in the same direction as explained before.As there is a negative voltage applied across the SCR’S T1 and T4, they are reverse biased and gets turned off when the current becomes zero or commutated.

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POWER CONVERTERS SIMULATION LAB (PG) OPERATION WITH R-L-E LOAD: Between ωt=0 and ωt = α , SCR’s T1 and T4are forward biased and are triggered simultaneously at α ,hence they get turned on. These thyristors conduct from α to π+α, forward biased SCR’s T1 and T4are triggered.The supply voltage turns off T1 and T4by natural commutation and the load current is transferred from thyristor,thyristor1 to T2 and T3. EXPERIMENTAL PROCEDURE: 1. To start Simulink click on the Simulink button on the MATLAB tool box (the library browser will be displayed) 2. Click on ‘new’ button on the library browser’s tool bar (an untitled blank window will appear). 3. Model the circuit by planning all its blocks from its corresponding library/tool box which is clearly shown in the table. 4. Circuit elements are organised by right clicking on the block. 5. Click on series RLC branch to get any one of the element i.e.,R,L,C which is required. 6. To change the circuit parameters applicable to the block by double clicking on the block/element and type the values. Keep the values default for some blocks like thyristor,diode,Mosfet etc., 7. To measure the voltage that es through the electrical devices. Connect voltage measurement block reset with the electrical block. 8. To observe the waveform in figure window scope block is connected with voltage measurement.This scope block is available by clicking on library browser. 9. To run the simulation,select simulation and then start.

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POWER CONVERTERS SIMULATION LAB (PG) CALCULATIONS: The average output voltage, 𝑉𝑑𝑐 = √2 ∙

𝑉𝑠(1+cos 𝛼)

--R Load

𝜋

𝑉𝑑𝑐 = 2√2 ∙

𝑉𝑠(cos 𝛼)

--R-L Load

𝜋

(Continuous current mode)

𝑉𝑑𝑐 = √2 ∙

𝑉𝑠(cos 𝛼−cos 𝛽)

-- R-L Load

𝜋

(Dis-continuous current mode)

𝑉𝑑𝑐 = 2√2 ∙

𝑉𝑠(cos 𝛼)

-- R-L-E Load

𝜋

(Continuous current mode)

𝑉𝑑𝑐 = √2 ∙

{𝑉𝑠(cos 𝛼−cos 𝛽)+𝐸(𝜋+𝛼−𝛽)} 𝜋

-- R-L-E Load (Dis-continuous current mode)

The extiction angle ᵝfound by sin(𝛽 − ∅) = sin(𝛼 − ∅)𝑒 𝑅(𝛼−𝛽)/𝜔𝐿

√2 ∙ 𝑉𝑠 ∙ sin

β−∅ Z

E

𝐸

--R-L Load

= (R) − {(𝑅) − (√2 ∙ 𝑉𝑠 ∙ 𝑠𝑖𝑛

𝛼−∅ 𝑍

} . 𝑒 (𝛼−𝛽) 𝑐𝑜𝑡 ∅

--R-L-E Load

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POWER CONVERTERS SIMULATION LAB (PG) SIMULATION RESULTS: Values of the Parameters

Calculated

Simulated

Vrms(v)

R(Ω)

L(mH)

E(V)

ᵝ

ᵝ

1

230

10

60

0

70°

2

230

10

60

0

70°

3

230

10

60

0

62°

5

220

0.06

0.85

87.31

60°

5

220

0.06

0.85

87.1

51.6°

6

220

0.06

0.85

60

60°

S.No

Edc(v)

Edc(v)

OUTPUT WAVEFORMS: FIG-1: R-LOAD AT α =70˚

FIG-3: RL LOAD AT α=62˚

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FIG-2: RL LOAD AT α =70˚

FIG-4: RLE DISCONTINUOS LOAD AT α=60˚

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) FIG-5: RLE CONTINUOUS LOAD AT α=51.6˚

FIG-6: RLE LOAD AT α=60˚

RESULT: The model of single phase full converter with R,RL,RLE load is created and simulated using MATLAB, corresponding waveforms at different firing angles and loads are observed simultaneously.

Faculty In-charge

7

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :2

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

THREE PHASE FULL CONVERTER AIM:Simulate a Three phase full converter with R & RL loads & find out the output voltageusing MATLAB software. . CIRCUIT DIAGRAM:

signal rms

Continuous powergui +

Gate pulse

Irms

i -

+

i In Mean

m

k

a

T5 g

a

g

a

T3

T1

g

k

m

k

m

Iavg

A

R = 10 ohm

signal rms

Vrms

+ v In Mean

V1 V2 V3 m

k a

a

a

g

T2 g

T6

T4

g

k

m

k

m

B

415 V, 50 Hz Three phase supply + v + v + v -

8

Vavg

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG)

THEORY AND OPERATION: The 3-Ø power circuit shown in the circuit diagram works as an 3-Ø AC to DC converter for firing angle delay 0<α≤90° and as 3-Ø Line commutated inverter for 0<α≤180°. The sequence of getting 6 SCR’s is 1,2,3,4,5,6 and for α=0°,T1T2T6 behave like diodes, T1 is triggered at ωt=30°; T2 at α=90°; T3 at α=150° and so on.The intervals between the SCR’s are fixed at an interval at 120° and negative group SCR’s are also fixed at the same interval i.e., 120°. Amongst them at any instant 2 SCR’s from each group must conduct.Initially T1 and T6 will be in operation as they are connected to A & B terminals,Vab appears

across the load.When T2 is triggered,T6 is

commutated as T1& T2 are connected to A & C terminals, Vab appears across the load.This sequence is followed for continuous triggering of SCR’s. EXPERIMENTAL PROCEDURE: 1. To start Simulink click on the Simulink button on the MATLAB tool box (the library browser will be displayed) 2. Click on ‘new’ button on the library browser’s tool bar (an untitled blank window will appear). 3. Model the circuit by planning all its blocks from irs corresponding library/tool box which is clearly shown in the table. 4. Circuit elements are organised by right clicking on the block. 5. Click on series RLC branch to get any one of the element i.e.,R,L,C which is required. 6. To change the circuit parameters applicable to the block by double clicking on the block/element and type the values. Keep the values default for some blocks like thyristor,diode, MOSFET etc., 7. To measure the voltage that es through the electrical devices. Connect voltage measurement block reset with the electrical block. 8. To observe the waveform in figure window scope block is connected with voltage measurement.This scope block is available by clicking on library browser.

9

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG)

TABULAR COLUMN FOR SWITCHING:

T1 30° 60° 90° 102°

0° 30° 60° 72°

T2 90° 120° 150° 162°

T3 150° 180° 210° 220°

T4 210° 240° 270° 282°

T5 T6 270° 330° 300° 360° 330° 390(30°) 342 402(12°)

R-LOAD:

0° 30° 60° 72°

T1

T2

1.67 3.33 5 5.67

5 8.33 11.67 15 18.33 6.67 10 13.33 16.67 20 8.33 11.67 15 18.33 21.6 9.01 12.35 15.69 19.03 22.37

T3

T4

T5

T6 Vo Calculated Vo Simulated 280 23.8 10.3 86.73

R-L LOAD:

S.NO. 1 2 3

10

0° 30° 60°

Vo Calculated Vo Simulated 280 23.09 10.3

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) THEORETICAL CALCULATIONS: For any α , 𝑉𝑜𝑎𝑣𝑔 =

3√3𝑉𝑚 cos 𝛼 𝜋

‘α’ OUTPUT WAVEFORMS: FIG-1: R-LOAD AT α=0˚

FIG-2: R-LOAD AT α=30˚

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for R & R-L Loads

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) FIG-3: R-LOAD AT α=60˚

FIG-5: R-L LOAD AT α=30˚

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) FIG-6: R-L LOAD ATα=60˚

RESULT: The model of three phase full converter with R &RL load is created and simulated using MATLAB, corresponding waveforms at different firing angles and loads are observed simultaneously.

Faculty In-charge

13

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :3

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

SINGLE PHASE AC VOLTAGE CONTROLLER AIM:Simulate single phase AC voltage controller with R &RL load usig matlab software. CIRCUIT DIAGRAM:

THEORY AND OPERATION: AC voltage controllers (ac line voltage controllers) are employed to vary the RMS value of the alternating voltage applied to a load circuit by introducing Thyristors between the load and a constant voltage ac source. The RMS value of alternating voltage applied to a load circuit is controlled by controlling the triggering angle of the Thyristors in the ac voltage controller circuits. In phase control the Thyristors are used as switches to connect the load circuit to the input ac supply, for a part of every input cycle. That is the ac supply voltage is chopped using Thyristors during a part of each input cycle.

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) The thyristor switch is turned on for a part of every half cycle, so that input supply voltage appears across the load and then turned off during the remaining part of input half cycle to disconnect the ac supply from the load. OUTPUT WAVEFORMS:

RESULT: Single phase ac voltage controller is simulated and corresponding waveforms are observed.

Faculty In-charge

15

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG)

Experiment No :4

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

THREE PHASE INVERTER WITH PWM CONTROL AIM: Simulate a Three phase inverter with pwm control and sketchthe output waveforms. SOFTWARE USED:MATLAB. CIRCUIT DIAGRAM :

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) SUBSYSTEM

THEORY AND OPERATION: Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a modulation technique used to encode a message into a pulsing signal. Although this modulation technique can be used to encode information for transmission, its main use is to allow the control of the power supplied to electrical devices, especially to inertial loads such as motors. In addition, PWM is one of the two principal algorithms used in photovoltaic solar battery chargers, the other being MPPT. The average value of voltage (and current) fed to the load is controlled by turning the switch between supply and load on and off at a fast rate. The longer the switch is on compared to the off periods, the higher the total power supplied to the load. The PWM switching frequency has to be much higher than what would affect the load (the device that uses the power), which is to say that the resultant waveform perceived by the load must be as smooth as possible. The term duty cycle describes the proportion of 'on' time to the regular interval or 'period' of

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) time; a low duty cycle corresponds to low power, because the power is off for most of the time. Duty cycle is expressed in percent, 100% being fully on. The main advantage of PWM is that power loss in the switching devices is very low. When a switch is off there is practically no current, and when it is on and power is being transferred to the load, there is almost no voltage drop across the switch. OUTPUT WAVEFORMS:

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POWER CONVERTERS SIMULATION LAB (PG) RESULT: Three Phase Inverter With Pwm Control is simulated and waveforms are observed.

Faculty In-charge

19

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :5

Class: M.Tech(PEED), I Sem DC-DC CONVERTER

AIM:Simulate DC-DC converter and sketchthe output waveforms. SOFTWARE USED:MATLAB. CIRCUIT DIAGRAM:

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A.Y:2015-2016

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) THEORY AND OPERATION: The Buck Converter is used in SMPS circuits where the DC output voltage needs to be lower than the DC input voltage. The DC input can be derived from rectified AC or from any DC supply.The buck Converter circuit consists of the switching transistor, together with the flywheel circuit (Dl, L1 and C1). While the transistor is on, current is flowing through the load via the inductor L1. The action of any inductor opposes changes in current flow and also acts as a store of energy. In this case the switching transistor output is prevented from increasing immediately to its peak value as the inductor stores energy taken from the increasing output; this stored energy is later released back into the circuit as a back e.m.f. as current from the switching transistor is rapidly switched off. When the switching transistor is switched on, it is supplying the load with current. Initially current flow to the load is restricted as energy is also being stored in L1, therefore the current in the load and the charge on C1 builds up gradually during the ‘on’ period. Notice that throughout the on period, there will be a large positive voltage on D1 cathode and so the diode will be reverse biased and therefore play no part in the action. When the transistor switches off, the energy stored in the magnetic field around L1 is released back into the circuit. The voltage across the inductor (the back e.m.f.) is now in reverse polarity to the voltage across L1 during the ‘on’ period, and sufficient stored energy is available in the collapsing magnetic field to keep current flowing for at least part of the time the transistor switch is open. The back e.m.f. from L1 now causes current to flow around the circuit via the load and D1, which is now forward biased.

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POWER CONVERTERS SIMULATION LAB (PG) OUTPUT WAVEFORMS:

RESULT: DC-DC converter is simulated and waveforms are observed.

Faculty In-charge

22

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :6

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

MODELLING OF SEPERATLY EXCITED DC MOTOR AIM: To built the Simulink model of D.C. motor and to the speed and torque characteristics for different values of voltage. CIRUIT DIAGRAM:

THEORY: For D.C. motor model The air gap flux  is proportional to field current

 = Kf If The torque Tm developed by the motor is proportional to the product of the armature current and air gap flux. Tm =k i k f i f i a For armature controlled dc motor the field current is kept constant, so Tm =km i a

(1)

Where km is torque constant The motor back emf being proportional to speed is given as Vb = K b w Where K b is back emf constant. The differential

23

equation of armature circuit

(2)

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) La

dia +Ra ia + vb = va dt

(3)

The torque equation is J

d 2 d +B = Tm 2 dt dt

Talking lap lace transforms of equation 1, 2, 3 assuming zero Initial conditions we get Vb(s) = kb w (s)

(4)

(Las + ra ) Ia (s) = Va (s) –Vb (s) (5) (js + B ) w (s) = Tm (s)

(6)

From equations 4, 5, 6 the system transfer function Is

w( s) va( s)

=

KM ( Ra  SLa )( JS  B)  K m K B )

PROCEDURE: 1. To start simulink click on simulink button on the MATLAB tool box (the library browser will be displayed) 2. Click the ‘new’ button on the library browser’s tool bar (an untitled blank window will appear). 3. Open the ‘source library ‘ and drag the step input block to your window. Double click on this block to the dialogue box. set the step time to 100 and set the initial value and final value to 1 to represent ‘unit step in input’. 4. Open the ‘continuous library’ and drag the transfer function block to your right of step input box block. Enter the numerator and denominator coefficients. 5. Open the ‘sinks library’ and drag the scope block to the right of transfer function block. 6. Using the left mouse button, click and drag from the step out put port to transfer function input port to connect them. Repeat the same to connect transfer function and scope blocks.

24

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POWER CONVERTERS SIMULATION LAB (PG) 7. Putt down ‘simulation’ menu bar and select ‘parameters’ set the parameters as below Start time

0

Stop time

20

Maximum step size

0.1

Minimum step size

0.01

Initial step size 0.01 and leave other parameter values at their default values. Press o.k. to close the dialog box. 1. Save your ‘model’. 2. Start the ‘simulation’ by once again pulling down the ‘simulation dialog box’. 3. Double click on the ‘auto scale’ icon (the response curve will be displayed). OBSERVATION: S NO

OUTPUT WAVEFORM:

25

Va (v)

W (rad/sec)

N (rpm)

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG)

RESULT: The speed for different values of voltage is simulated with the simulink model of D.C.motor.

Faculty-Incharge

26

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :7

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

TRANSFER FUNCTIOIN OF STATIC VARIABLE MODEL AIM: Write aprogram and Simulate the given model and representing its I-O model,State variable method and to observe the time domain specifications of each model, for a given transfer function. 2𝑠 3 + 7𝑠 2 + 12𝑠 + 8 8𝑠 3 + 6𝑠 2 + 11𝑠 + 9 SOFTWARE USED:MATLAB PROGRAMS: Transfer function to state space model clc;clear all;close all; a = [2 7 12 8]; b = [1 6 11 9]; c = tf(a,b); [A,B,C,D]= tf2ss(a,b); disp(A); disp(B); disp(C); disp(D);

State space model to transfer function clc;clear all;close all; A = [0 1 0;0 0 1;-9 -11 -6]; B = [0 0 1]'; C = [-10 -10 -5]; D = [2]; [b a] = ss2tf(A,B,C,D); x =tf(b,a); %%disp(x); stepinfo(x);

27

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) THEORY: Transformation: Transfer Function ↔ State Space Two of the most powerful (and common) ways to represent system are the transfer function form and the state space form. This page describes how to transform a transfer function to a state space representation, and vice versa. Converting from state space form to a transfer function is straightforward because the transfer function form is unique. Converting from transfer function to state space is more involved, largely because there are many state space forms to describe a system. STATE SPACE TO TRANSFER FUNCTION Consider the state space system:

Now, take the Laplace Transform (with zero initial conditions since we are finding a transfer function):

We want to solve for the ratio of Y(s) to U(s), so we need so remove Q(s) from the output equation. We start by solving the state equation for Q(s)

The matrix Φ(s) is called the state transition matrix. Now we put this into the output equation

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Now we can solve for the transfer function:

Note that although there are many state space representations of a given system, all of those representations will result in the same transfer function (i.e., the transfer function of a system is unique; the state space representation is not). TRANSFER FUNCTION TO STATE SPACE MODEL STATE SPACE MODELS OF SYSTEMS ARE NOT UNIQUE; A SYSTEM HAS MANY STATE SPACE REPRESENTATIONS. Probably the most straightforward method for converting from the transfer function of a system to a state space model is to generate a model in "controllable canonical form." This term comes from Control Theory but its exact meaning is not important to us. To see how this method of generating a state space model works, consider the third order differential transfer function:

We start by multiplying by Z(s)/Z(s) and then solving for Y(s) and U(s) in of Z(s). We also convert back to a differential equation.

We can now choose z and its first two derivatives as our state variables

29

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) From these results we can easily form the state space model:

For a general nth order transfer function:

the controllable canonical state space model form is

MATLAB uses a variant of the controllability canonical form in its "ss2tf" function.

RESULT: Transfer Function of Static Variable Modelis simulated and waveforms are observed.

Faculty In-charge

30

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :8

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

FREQUENCY RESPONSE ANALYSIS AIM: Write a program and simulate the given system in Nyquist,Bode ,Root Locus plots and observe the response of each plot, for a give transfer function.

GH =

10 [𝑠(1+0.5𝑠)(1+0.05𝑠)]

SOFTWARE USED: MATLAB THEORY: ROOT LOCUS Root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a system. This is a technique used as a stability criterion in the field of control systems developed by Walter R. Evans which can determine stability of the system. The root locus plots the poles of the closed loop transfer function in the complex S plane as a function of a gain parameter. In addition to determining the stability of the system, the root locus can be used to design the damping ratio (ζ) and natural frequency (ωn) of a system. PROGRAM: clc; clear all; close all; s = tf('s'); GH = 10/(s*(1+0.5*s)*(1+0.05*s)); rlocus(GH); grid on; BODE PLOT A Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. Both quantities are plotted against a horizontal axis proportional to the logarithm of frequency.

31

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) 1. Gain Margin: Greater will the gain margin greater will be the stability of the system. It refers to the amount of gain, which can be increased or decreased without making the system unstable. It is usually expressed in dB. 2. Phase Margin: Greater will the phase margin greater will be the stability of the system. It refers to the phase which can be increased or decreased without making the system unstable. It is usually expressed in phase. 3.Gain Cross Over Frequency: It refers to the frequency at which magnitude curve cuts the zero dB axis in the bode plot. 4.Phase Cross Over Frequency: It refers to the frequency at which phase curve cuts the negative times the 180 degree axis in this plot. PROGRAM: clc; clear all; close all; s = tf('s'); GH = 10/(s*(1+0.5*s)*(1+0.05*s)); bode(GH); grid on; [gm,pm,w,wcg]=margin(GH) disp('gain margin is'); disp(gm); disp('phase margin is'); disp(pm); disp('gain crossover is'); disp(w); disp('phase crossover is'); disp(wcg);

32

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) NYQUIST STABILITY CRITERIA 1. Defining the Nyquist path in the z -plane that encloses the exterior of the unit

circle. Here the region to the left of a closed path is considered to be enclosed by that path when the direction of the path is taken anticlockwise. 2. Mapping the Nyquist path in z -plane onto the GH(z) plane which results in Nyquist plot of GH(z). 3. Stability of the closed loop system is investigated by studying the behavior of Nyquist plot with respect to the critical point (-1, j0) in the GH(z) plane. PROGRAM: clc; clear all; close all; s = tf('s'); GH = 10/(s*(1+0.5*s)*(1+0.05*s)); nyquist(GH); grid on; [gm,pm,w,wcg]=margin(GH) disp('gain margin is'); disp(gm); disp('phase margin is'); disp(pm); disp('gain crossover is'); disp(w); disp('phase crossover is'); disp(wcg);

33

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) OUTPUT WAVEFORMS: a) ROOT LOCUS PLOT

b)BODE PLOT

34

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) c) NYQUIST PLOT

RESULT: Frequency Response

Analysis(Nyquist,Bode ,Root Locus plots)is

simulated and waveforms are observed.

Faculty In-charge

35

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :9

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

DESIGN OF COMPENSATOR AIM: To design a compensator for a given system using linear time invariant method, SISO tool and by writing a program for the transfer function for required specifications. SOFTWARE USED:MATLAB CIRCUIT DIAGRAM:

PROGRAM: g = tf(1,[1 1 1]); k = 6.8 z = 5.298 c = tf(k*[1 z],1) x = (c*g,1) step(g) %%disp(x); step(x)

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) OUTPUT WAVE FORMS: a) LTI METHOD:

b) STEP RESPONSE

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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) c) OPEN LOOP ROOT LOCUS & BODE PLOTS

RESULT: Compensator for a given system using linear time invariant method, SISO toolis simulated and waveforms are observed.

Faculty In-charge

38

HOD-EEE

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) Experiment No :10

Class: M.Tech(PEED), I Sem

A.Y:2015-2016

Program to Solve Swing Equation using Point-by-Point Method

Aim:To solve the swing equation of the given problem by using Point-by-Point method and write a MATLAB program to the result. PROBLEM: A 20 MVA, 50Hz generator delivers 18MW over a double circuit line to an infinite bus. The generator has KE of 2.52MJ/MVA at rated speed. The generator transient reactance is Xd=0.35p.u. Each transmission circuit has R=0 and a reactance of 0.2pu on 20 MVA Base. |E|=1.1 p.u and infinite bus voltage V=1.0. A three phase short circuit occurs at the midpoint of one of the transmission lines. Plot swing curves with fault cleared by simultaneous opening of breakers at both ends of the line at 6.25 cycles after the occurrence of fault. Also plot the swing curve over the period of 0.5 s if the fault sustained. Solve the swing equation by point-by-point method theoretically and using MATLAB Program. Comment on system stability.

MATLAB PROGRAM:

Program 1: Save this part in another m-file with name swing.m %Defining the function swing function[time ang]=swing(tc) k=0;v=1;E=1.1;pm=0.9;T=0.5;delT=0.05;ddelta=0;time(1)=0;ang(1)=21.64;xdf=1 .25;xaf=0.55;t=0; delta=21.64*pi/180;i=2; m=2.52/(180*50); while t
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G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG) time(i)=t; ang(i)=deltadeg; i=i+1; end end Program 2: Main program that is dependent on swing.m %solution of Swing equation by point-by-point method clc clear all close all for i=1:2 tc=input('enter the value of clearing time:\n'); [time,ang]=swing(tc) t(:,1)=time; a(:,i)=ang; end plot(t,a(:,1),'*-',t,a(:,2),'d-') axis([0 0.5 0 inf]) t,a Inputs to main program: Enter the value of clearing time as 0.25 sec, and 5 sec

40

G.N.I.T.S – EEE DEPARTMENT

POWER CONVERTERS SIMULATION LAB (PG)

EXPECTED OUTPUT: swing equation by point by point method 200

stable for 6.25 cycle CB

d e g r e e s

160

A n g l e

i n

180

140

unstable for sustained fault (tc=5sec)

120 100 80 60 40 20 0 0

0.1

0.2 0.3 time in seconds

0.4

0.5

RESULT: The solution for swing equation is done by using point by point method by taking a problem as an example and its corresponding graph is plotted.

Faculty In-charge :

41

HOD-EEE