University of Manitoba

Department of Electrical & Computer

Engineering

ECE 4600 Group Design Project

Final Project Report

Synchronous Generator Excitation System

by

Group 07

Marko Pujic

Kashif Khokhar

Mufeed Al Khater

Falaah Alshammari

Abdulelah Alangari

Academic Supervisor

Athula Rajapakse, Ph.D., P.Eng

Date of Submission

March 2, 2016

Copyright © 2016 Marko Pujic, Kashif Khokhar, Mufeed Al Khater, Falaah

Alshammari, Abdulelah Alangari

ii

Abstract

The purpose of this project was to design and implement an excitation system for 1.5 KVA,

60Hz, 208V, 3- phase synchronous generator to automatically regulate the terminal voltage. The

focus was designing a static exciter since it has a faster transient response to changes in load or

reference voltage. The excitation system was divided into specific blocks. Specifically, the AVR

(microcontroller); firing circuit; measuring elements; AC to DC variable convertor; and an initial

start-up battery and charging station. Protection was implemented to ensure the DC current

injected into the field winding did not exceed the rated value.

Excitation system was successfully implemented. Upon initial start up the generator takes

approximately 5 seconds to build voltage of the generator up to the reference voltage. Excitation

system takes about 5 seconds to reach the steady state when a step change is applied to the

reference voltage. Tests indicated that the steady state error of the generator terminal voltage was

within ±3 % of the reference voltage for a specified voltages between 50 to 190 .

iii

Contributions

Legend: Lead task Contributed

Mu

feed

Alk

hate

r

Ka

shif

Kh

ok

har

Fa

laa

h A

lsh

am

mari

Ab

du

lela

h A

lan

gari

Ma

rko

Pu

jic

Open & Short Circuit Test for Excitation

System o o o o

Measurements and controller feedback design o

Design of a digital control system

MatLab simulation of the control system

Automatic Voltage Regulator design and

testing o

Simulation Using PSCAD o o

Generator battery start-up o o

Double pole double throw relay Design o

Recharging System

Buck Converter, Rectifier o o

IGBT isolated firing circuit design and

implementation o o

Testing the Excitation System o o o o

Generator protection o

Thermal protection design

Hardware circuit design fabrication and testing o o o o

Literature review o o o

Final report o o o o o

iv

Acknowledgements

We would like to thank all the following individuals; without them this project would not have

been completed successfully:

Dr. Rajapakse Athula (Our academic supervisor) for his support and advice throughout the

project;

Erwin Dirks for his help with ordering parts and technical support;

Dr. Oliver Derek for coordinating Capstone;

Daniel Card for his advices and technical feedback;

Aidan Topping for technical communications feedback;

ECE Tech Shop for the support with parts providing;

v

Contents

Abstract ............................................................................................................................................ ii

Contributions .................................................................................................................................. iii

Acknowledgements ......................................................................................................................... iv

Nomenclature ................................................................................................................................. vii

List of Figures ................................................................................................................................. ix

List of Tables .................................................................................................................................. xi

Chapter 1 .......................................................................................................................................... 1

1.1 Synchronous Generator Excitation System............................................................................ 1

1.1.1 Synchronous Generator Operating Principle .................................................................. 1

1.1.2 Role of the Exciter .......................................................................................................... 2

1.1.3 Different types of excitation systems .............................................................................. 2

1.2 Project Objectives ................................................................................................................ 3

1.2.1 Purpose ............................................................................................................................ 3

1.2.2 Project specifications ...................................................................................................... 3

1.3 Overview of the design .......................................................................................................... 4

1.3.1 Overall structure of excitation system ............................................................................ 4

1.3.2 Automatic voltage regulator (AVR) ............................................................................... 5

1.3.3 Rectifier........................................................................................................................... 5

1.3.4 Buck converter ................................................................................................................ 5

1.3.5 Start-up Battery and Charger .......................................................................................... 5

1.3.6 Measuring Elements ........................................................................................................ 5

1.3.7 Firing Circuit ................................................................................................................... 5

1.4 Design and Analysis Tools Used ........................................................................................... 5

1.4.1 PSCAD ............................................................................................................................ 6

1.4.2 Matlab ............................................................................................................................. 6

1.4.3 Arduino UNO .................................................................................................................. 6

Chapter 2 Design of the Power Electronics System ..................................................................... 7

2.1 Obtaining Synchronous Generator Parameters ...................................................................... 7

2.2 Design of AC to Variable DC Converter ............................................................................. 10

2.2.1 Rectifier......................................................................................................................... 10

2.2.2 Buck Converter ............................................................................................................. 11

2.2.3 Inductor and Capacitor Selection .................................................................................. 11

2.2.4 Simulation Results ........................................................................................................ 15

vi

2.3 Design of Feedback Controller ...................................................................................... 17

2.3.1 Measuring Elements for feedback control .................................................................... 17

2.3.2 PI Controller for Automatic Voltage Regulator ............................................................ 19

2.3.3 Selection of controller parameters ................................................................................ 20

2.3.4 Simulation results .......................................................................................................... 22

2.4 Design of Protection and Safety Features ...................................................................... 26

2.4.1 Firing Circuit Isolation .................................................................................................. 26

2.4.2 Generator Protection ..................................................................................................... 28

2.4.3 Thermal Protection of IGBT's - Heat Sink Design ....................................................... 28

2.4 Design of Start-up Power Supply................................................................................... 31

2.4.1 Selection of Battery ....................................................................................................... 33

2.4.2 Battery Charger ............................................................................................................. 34

Chapter 3 Design of a Digital Control System ........................................................................... 40

3.1 Functions and Requirements of the Digital Controller ........................................................ 40

3.2 Factors Considered in Selection of Microcontroller ............................................................ 40

3.3 Peripheral Hardware ............................................................................................................ 41

3.4 Analog to Digital Conversion .............................................................................................. 42

3.5 Digital to Analog Conversion .............................................................................................. 43

Chapter 4 Design of Control Software Program ......................................................................... 44

4.1 System Initialization ............................................................................................................ 44

4.2 Switching ............................................................................................................................. 45

4.3 Updating Reference Voltage/LCD ....................................................................................... 46

4.4 PI Controller ........................................................................................................................ 46

Chapter 5 Fabrication and Testing .............................................................................................. 48

Chapter 6 Conclusion ................................................................................................................. 53

Bibliography .................................................................................................................................. 54

Appendix A .................................................................................................................................... 56

Appendix B .................................................................................................................................... 61

Appendix C .................................................................................................................................... 64

Appendix D .................................................................................................................................... 71

Appendix E .................................................................................................................................... 73

Appendix F .................................................................................................................................... 80

G07_FinalReoprt List of Erratum

Section# Page# Error Correction 2.1 9 Can be found in the appendix. Can be found in the appendix A. 2.3.1 18 H bridge rectifier in figure (2.2.1) H bridge rectifier in figure 2.3.1 2.3.1 18 Equation 2.3.3 Vrms = 2 ∗ Vpeak

√2 = 2 ∗ 20√2= 28.28

Vrms = 2 ∗ Vpeak√2 = 2 ∗ 23.1

√2= 32.66 2.3.2 20 The simplified simulation model is shown The simplified simulation model figure 2.3.5 is shown 2.3.2 20 code is provided in Appendix C. code is provided in Appendix D. 2.3.4 22 Simplified model shown in figure 2.3.4 Simplified model shown in figure 2.3.5 2.3.4 22 The PI controller in figure 2.3.5 The PI controller in figure 2.3.7 2.3.4 22 Figure 2.3.6 shows the PI Figure 2.3.7 shows the PI 2.4.3 29 Figure 2.4.3: Thermal Resistance Circuit [REFERENCE] Figure 2.4.3: Thermal Resistance Circuit [14] 2.4 31 TITLE: 2.4 Design of Start-up Power Supply TITLE: 2.4.4 Design of Start-up Power Supply 2.4.4 31 As seen in figures 2.4.2 and 2.4.3 As seen in figures 2.4.6 and 2.4.7 2.4.4 31 Shown in figure 2.4.1 is the Shown in figure 2.4.5 is the 2.4.5 33 TITLE: 2.4.1 Selection of Battery TITLE: 2.4.5 Selection of Battery 2.4.5 33 Referring to figure 2.4.4, two Referring to figure 2.4.8, two 2.4.6 34 TITAL: 2.4.2 Battery Charger TITLE: 2.4.6 Battery Charger 2.4.6 35 shown below in figure 2.4.6 shown below in figure 2.4.10 2.4.6 35 According to figure 2.4.5 According to figure 2.4.9 2.4.6 36 The circuit in figure 2.4.7 is the The circuit in figure 2.4.11 is the 2.4.6 36 Labeled circuit figure 2.4.8 Labeled circuit figure 2.4.12 2.4.6 38 Referring to figure 2.4.10 Referring to figure 2.4.13 2.4.6 38 Referring to figure 2.4.11 Referring to figure 2.4.14 3.2 40 Figure 3.1 Figure 3.2 3.2 41 Figure 2.2: Arduino Uno Figure 3.2: Arduino Uno 4 44 Figure 3.1: Main Flowchart. Figure 4.1: Main Flowchart. 4.4 46 Equation 2.3.6 was used Equation 4.1 was used 4.4 46 Equation 4.4 shows the implementation Figure 4.4 shows the implementation App. A 56 The line measured using figure … The line measured using figure 2.1.3

vii

Nomenclature Idc DC Current

KI Integral Gain

Kp Proportional Gain

Vac Alternating Voltage

Vdc DC Voltage

Vl-l Line-to-Line Voltage

Vref Voltage reference (AVR)

viii

VRMS Root Mean Squared (RMS) Voltage

Vt Generator terminal voltage

AC Alternating Current

A/D Analog to Digital Converter

Ah Amp-Hour

AVR Automatic Voltage Regulator

BJT Bipolar Junction Transistor

DAC Digital to Analog Converter

DC Direct Current

DPDT Double Pole Double Throw

LCD Liquid Crystal Display

IGBT Insulated Gate Bipolar Transistor

OCRA Output Compare Register A

PI Proportional Integral

PSCAD Simulation Software - Power Systems

PWM Pulse-Width Modulation

NiCD Nickel Cadmium

NiMH Nickel-Metal Hydride

SLA Sealed Lead-acid

VRLA Valve Regulated Lead-acid

ix

List of Figures 1.1 The per-phase equivalent circuit of a synchronous generator................................ 2

1.3 Block diagram of the overall design ……………………………………............. 4

1.3.1 Closed loop control diagram…………………………………………………….. 4

2.1.1 Line Voltage vs. Field DC Current, and Line Current vs. Field DC Current for the

Open and Short Circuit Tests…………………………………………………

8

2.1.2 Saturated and Unsaturated Xs with the change of Armature Current …………. 8

x

2.1.3 The step response of the DC field winding………………………………………. 9

2.2.1 A schematic of three phase bridge rectifier…………………………………………. 10

2.2.2 A snapshot of the rectifier used in our project ……………………………………. 11

2.2.3 DC-DC Buck Converter………………………………………………………….. 14

2.2.4 The DC-DC Buck Converter in our project………………………………. 14

2.2.5 Rectifier and buck converter simulated circuit…………………………………... 15

2.2.6 IGBT Firing circuit with 0.069 duty cycle………………………………………... 15

2.2.7 Simulation graph of the rectifier and the buck converter design…………………. 16

2.3 Open loop diagram……………………………………………………………. 17

2.3.1 Measuring element………………………………………………………... 19

2.3.2 Root locus of simplified simulation model........................................................... 21

2.3.3 Root locus of simplifie simulation model with Kp = 0.0002................................ 21

2.3.4 Step response of simulation model with PI controller........................................ 22

2.3.5 Simplified simulation model……………………………………………… 23

2.3.6 PWM firing Signal for the IGBT…………………………………………………. 23

2.3.7 PI Controller Circuit…………………………………………………………… 23

2.3.8 The settling time of the PI controller……………………………………………... 24

2.3.9 The response of the PI controller while running the converter…………… 25

2.4.1 Complete schematic diagram of the IGBT gate driver circuit……………………. 26

2.4.2 PWM signal from the Microcontroller and the MIC5021……………………….. 27

2.4.3 Thermal Resistance Circuit………………………………………………….. 29

2.4.4 Calculated size heat sink………………………………………………………… 31

2.4.5 Controlling circuit of the DPDT relay …………………………………………….. 32

2.4.6 Normally closed position......................................................................................... 32

2.4.7 Schematic while battery is attached................................................................... 33

2.4.8 12V SLA batteries with high voltage diode between……………………………... 34

2.4.9 Pin labelled drawing of L200C……………………………………………………. 35

2.4.10 Battery charging circuit............................................................................................. 35

xi

2.4.11 Nodal analysis at the labelled node yields shown equation. A variable resistance

would account for a variable voltage charger..........................................................

37

2.4.12 High power ceramic resistor………………………………………………………. 37

2.4.13 Completed battery recharging station…………………………………………… 39

2.4.14 Demonstrating that the output of the charger is charging the battery by showing on

the multimeter a voltage higher than that of the battery's………………………

39

3.2 Arduino UNO……………………………………………………………… 41

3.3 LCD..................................................................................................................... 42

4.1 Main flowchart.................................................................................................... 44

4.2 Switching flowchart.............................................................................................. 45

4.3 PI controller........................................................................................................ 47

5.1 Controller behavior for start-up of the machine................................................... 48

5.2 Step response of excitation system to change in reference from 100Vl-l to 190Vl-l... 49

5.3 LCD displaying Vref and Vt...................................................................................... 49

5.4 Step response of excitation system to change in reference from 190Vl-l to 100Vl-l 50

5.5 LCD displaying Vref and Vt.................................................................................... 50

5.6 Step response of excitation system to change in reference from 100Vl-l to 50Vl-l 51

5.7 LCD displaying Vref and Vt.................................................................................... 51

5.8 Response of the excitation system with addition of an inductive load.................. 52

5.9 Response of the excitation system with addition of an capacitive load.................. 52

A.2.1 Load Angle Characteristics Curve for the Synchronous Generator. 63

List of Tables

1 Design specifications............................................................................................... 3

2 Open and short circuit test results............................................................................ 61

3 Calculating saturated and unsaturated armature reactance...................................... 61

4 Load test results....................................................................................................... 62

5 Load angle calculation results................................................................................. 63

xii

6 PWM signal error.................................................................................................... 64

1

1

Chapter 1

1.1 Synchronous Generator Excitation System

The main function of the excitation system is to provide DC current to the field winding of the

synchronous generator. The excitation system regulates the generator output.

1.1.1 Synchronous Generator Operating Principle

The synchronous generator is essentially used to convert mechanical power to AC electrical

power. The synchronous generator consists of a rotating component called a rotor and a stationary

component called stator. The rotor contains the field winding that produces the magnetic field in

the machine. The stator contains an armature winding in which the electromotive force (emf) is

induced figure1.1.1.

By supplying the rotor with DC current the rotor magnetic field is energized. The prime mover

will then spin the rotor at synchronous speed producing a rotational magnetic field in the

machine, which induces emf in the stator winding [16].

Induced emf in the coil is given by:

sin (1.1.1)

and the per phase voltage (no load) is obtained from:

= 4.44 . (1.1.2)

Finally, synchronous speed of the rotor in (rpm) is given by:

(1.1.3)

Variables are defined as: is a pitch factor, is the flux per pole, is the angular frequency,

is the number poles in the machine, is the frequency of the induced emf. is the number of

turns in the coil, and effective turns per phase.

2

Figure 1.1.1: The per-phase equivalent circuit of a synchronous generator

1.1.2 Role of the Exciter

The role of the exciter was to provide DC current to the field winding.

1.1.3 Different types of excitation systems

Excitation systems can be classified into three types: DC excitation systems, AC excitation

systems, and static excitation systems.

• DC excitation system:

DC exciter uses a dc generator as a source of power and provides current to the rotor through

slip rings. The shaft of the main generator or a motor may be used to drive the exciter. This

exciter is either self-excited or separately excited.

• AC excitation system

AC exciter uses an AC machine as a source of power. The AC output is rectified to produce

DC current for the field winding. This exciter is consisting of two different types of

rectifiers; stationary and rotating. There are two types of AC excitation systems: Stationary

AC and Brushless AC excitation system.

• Static excitation system

The static exciter uses power electronic devices to rectifier the main generators voltage and

feeds it back to the field winding. Static exciter has fastest transient response compared to

other excitation system.

Stator

Rotor

3

1.2 Project Objectives

The project objective was to design and implement an excitation system for 1.5 KVA, 60Hz,

208V, 3- phase synchronous generator. The static exciter was implemented by using power

electronic devices. The supply for the excitation system was obtained by rectifying the terminal

voltage from the generator. Microcontroller was used to implement the AVR. Design and

implementation of a variable AC to DC convertor was completed. Protection was added to

ensure no damage to field winding. External battery was used for initial start-up and a charging

was designed to charge the battery.

1.2.1 Purpose

The implementation of a static exciter in the excitation system allows for faster transient response

to system changes. The automatic voltage regulator ensures that the terminal voltage being

supplied to a load was equal to the reference voltage specified by a user. Regulating the voltage at

specified value prevents damage to the attached load and may reduce reactive power losses.

1.2.2 Project specifications

Excitation system design specifications are listed in Table 1. The static exciter provided DC

voltage to the field winding. AVR regulated the terminal voltage of the synchronous generator to

within the accepted 5% tolerance of the reference voltage. IGBT was used as an electronic switch

for the buck converter with a switching frequency of 15 KHz. The buck converter was capable of

operating between 24-volt DC to 80-volt DC. The measuring element was designed to convert

the full range of terminal voltage to a RMS value between 0 to 4.1 V DC that was sent to the

microcontroller.

Feature Value or Range

IGBT switching frequency 15KHz

Microcontroller sampling rate 9600Hz

AVR 50 to 190 volt

Output DC voltage to field winding 24 to 80 volt

Output DC current 0 to 0.9 A

Settling time 5 sec

Steady state error ±5%

Table 1: Design specifications.

4

1.3 Overview of the design

Figure 1.3 shows the overall design of the synchronous excitation system. The batteries were

used to provide initial DC current to the field winding. The static exciter was connected to the

field winding after initial excitation and DC current was supplied to the field winding. The

amount of DC current being supplied was controlled by the AVR.

Figure 1.3: Block diagram of the overall design

1.3.1 Overall structure of excitation system

The design of the excitation system consisted of an automatic voltage regulator (AVR),

measuring element and a static exciter. The AVR was implemented using a microcontroller. The

measuring element was designed using a rectifier transformer, rectifier and a voltage divider. The

static exciter was designed using power electronic devices such as a rectifier and buck converter.

Figure 1.3.1 shows the control diagram of the excitation system.

Error

Desired

Input

Respons

e _

Automatic

Voltage

Regulator

Exciter

Generator

Measuring Element

Actual

Output

Figure 1.3.1: Closed loop control diagram.

5

1.3.2 Automatic voltage regulator (AVR)

Automatic voltage regulator compared the RMS (root mean square) output voltage of the

generator with a reference voltage. The difference between the measurements was corrected

using a PI (proportional gain plus integral) controller which adjusted the duty cycle of the PWM

(pulse width modulation).

1.3.3 Rectifier

A 3 Phase uncontrolled full wave bridge rectifier was used to convert the output of the generator

from AC to a DC voltage.

1.3.4 Buck converter

The buck converter controlled the output DC voltage from the rectifier and filtered out high order

harmonics. The desired output voltage was based on Equation 1.3.4, D in the equation represents

the duty cycle [1].

(1.3.4)

1.3.5 Start-up Battery and Charger

The purpose of rechargeable battery was to provide a DC voltage to the field winding. The

battery was connected to a charging station to recharge the battery.

1.3.6 Measuring Elements

Measured the terminal voltage from the generator and converted the voltage to RMS and

provided this measurement to the microcontroller.

1.3.7 Firing Circuit

The function of the firing circuit was to provide the IGBT with the PWM signal and isolation for

the microcontroller from the rest of the system.

1.4 Design and Analysis Tools Used

Analysis tools consisted of using PSCAD supplied in the lab for simulation. Matlab to find PI

parameters, and the Arduino UNO as the AVR and monitor for several components which is

described in subsequent chapters.

6

1.4.1 PSCAD

PSCAD is the main software that was used in our project to simulate several components to test

the design prior building the real circuits and improve the design efficiency. Before building our

project on hardware we simulated the buck converter and the rectifier and we obtained the desired

values that are ready to be applied practically. A PI controller was also tested and tuned on

PSCAD through the adjustment through Matlab values for the proportional gain and proportional

integral were found.

1.4.2 Matlab

Matlab was used to graph the root locus of the simplified simulation model. The root locus plot

was used to determine preliminary values graphically of the proportional gain and integral

parameters. These results were used initially to tune the PI controller in PSCAD.

1.4.3 Arduino UNO

The serial monitor was used to track and verify input and output of the microcontroller through

the serial USB connection. The PWM output and the terminal voltage were monitored. An open

loop test was performed on the controller and values are displayed on the serial monitor. The

serial commands were removed from the program so they did not affect the performance of the

system.

7

Chapter 2 Design of the Power Electronics System

2.1 Obtaining Synchronous Generator Parameters

To calculate the synchronous generator parameters the following three tests were performed: DC

step response, open circuit test and short-circuit test. The inductance and the resistance of the

field winding for the synchronous generator were calculated from the DC step response test. The

open circuit test was performed in order to find the internal generated voltage of the generator for

any given field current. The short-circuit test provided information about the current capabilities

of a synchronous generator. The capability curve was constructed from the values obtained from

the open and short circuit test.

Open Circuit Test

We initially performed this test by disconnecting the terminals of the synchronous generators

from all loads and then setting the field current to zero and the rated speed at 1800 rpm. Then by

increasing the field current the terminal voltage was measured at each step along the way. Thus

we obtained the relationship between the field current and the terminal voltage.

Short-Circuit Test

We initially performed this test by short-circuit the terminals of the synchronous generators and

then adjust the field current to zero and the rated speed at 1800 rpm. We recorded the armature

current Ia as the field current is increased. Thus we obtained the relationship between the field

current and the armature current Ia.

DC Test for the armature winding:

The main reason of the DC test of the armature winding is to determine the armature resistance

Ra. A variable DC voltage was applied between the two stator terminals.

VDC = 37 V and IDC = 3 A:

(2.1.1)

Hence, the per phase stator resistance if the stator connected as:

Y-connected => Ra =

(2.1.2)

Δ-connected =>

(2.1.3)

8

Figure 2.1.1: Line Voltage vs. Field DC Current, and Line Current vs. Field DC Current for the Open and Short Circuit

Tests

Figure 2.1.2: Saturated and unsaturated Xs with the change of armature current

-0.5

0.5

1.5

2.5

3.5

4.5

5.5

-50

50

150

250

350

450

550

0 0.2 0.4 0.6 0.8 1 1.2

V_L

L [v

olt

]

If [Amp]

OCC vs. SCC

air gap line

Open Circuit Test

Short Circuit Test

Ideal Short Circuit Test

I a [

Am

p]

0

2

4

6

8

10

12

14

16

18

20

22

24

26

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Xs

[Oh

m]

Ia [Amp]

Saturated and Unsaturated Xs Vs. Is

Saturated Armature Reactance (Xs)

Unsaturated Armature Reactance (Xs)

9

DC Test for the field winding:

This test was performed to find the inductance and resistance of the field winding. These

parameters were needed to model the exciter. A 20-volt DC step was applied to the field

winding and the response was measured using an oscilloscope. The step response of the field

winding is shown in figure 2.1.3. The current reached steady state at 360.352 ms with a value

of 0.25 A and the measured voltage was 20.58V. Equation 2.1.4 shows the resistance of the

field winding.

(2.1.4)

The value of the inductance calculated was 6.18 H. The complete calculation can be found in the

appendix.

(2.1.5)

Figure 2.1.3: Step response of DC field winding.

10

2.2 Design of AC to Variable DC Converter

The AC to variable DC converter was designed using a three-phase uncontrolled rectifier,

100μF capacitor and a buck convertor. The capacitor reduced voltage ripple from the rectified

signal and the buck convertor was used to control DC voltage.

2.2.1 Rectifier

A rectifier is a power electronic device which convert AC voltage to DC voltage. There are

two types of three phase rectifiers controlled and uncontrolled rectifiers. Originally, the

proposed design required a controlled rectifier which contained 6 IGBTs. The design was

changed to an uncontrolled diode rectifier. Equation 2.1.1 shows the rectified voltage assuming

that the terminal voltage is 208 . Figure 2.2.1 shows the three phase bridge rectifier

(36MT120) which was rated for 35A.

(2.2.1)

Figure 2.2.1: Schematic of a three phase bridge rectifier[1].

11

Figure 2.2.2: A snapshot of the rectifier used in our project.

2.2.2 Buck Converter

A buck converter is a step-down DC -DC converter. The buck converter consisted of a

diode, inductor, capacitor and an electronic switch. The IGBT is a semiconductor device

which was used as an electronic switch. In our design we used the IXGH6N170A-IGBT

model which had high current handling capability (6 A). Free-wheeling diode was used to

provide protection for the IGBT from being damaged by reverse current from the

inductive load. The diode used was the TO-220 FULL-PAK model cause of the short

reverse recovery time and low forward voltage drop.

2.2.3 Inductor and Capacitor Selection

The calculated values of three different scenarios were considered in the selection of the

components for the buck convertor. The first case considered was the outcome of supplying the

buck convertor with DC value of the rated voltage of 208V line to line and a field current of

0.9A. The second scenario considered was supplying a DC voltage based on 85V line to line.

12

The duty cycle needed to increase the DC field voltage in order to restore the terminal voltage

to rated value was calculated. The final outcome considered was feeding the buck convertor

with the equivalent DC voltage of 260V line to line. The reduction of the duty cycle that was

need in order to reduce the terminal voltage to rated value was calculated. Scenario #3 shown

below was a sample of the calculation and the remaining calculations can be found in Appendix

A.

Scenario Case #3:

Output voltage of the synchronous generator: 260 V

Vphase =

= 150 V (2.3.1)

Voltage after the Diode rectifier:

We need to reduce the field current to about 0.3 A at the output of the buck regulator so

the voltage at the field winding will be

=

=

= 0.069 (2.3.2)

Inductor Selection:

Lmin =

=

= 37.70mH, is switching frequency. (2.3.3)

IL = IR =

=

= 0.3A (2.3.4)

Imax = IL +

, = 5% A (2.3.5)

Imax = 0.3 A +

= 0.3075A (2.3.6)

Imin = IL -

= 0.2925A (2.3.7)

L =(

) = (

) = 1.49H (2.3.8)

The inductor must be rated for rms current,

13

IL, rms =

=

= 0.3A (2.3.9)

The inductor voltage when the switch is closed is = 350 – = 325.7V

The inductor voltage when the switch is open is = V

Capacitor Selection:

Voltage ripples is

, Let’s choose it to be 10 %

C =

=

= 0.781 (2.3.10)

The initial selection of the inductor was based on a switching frequency of approximately 1

kHz. The size of the inductor at this frequency was 1.49 H. The cost of this inductor did not

fall within the project budget it was decided to increase the frequency to 15 kHz to reduce the

size of the inductor. Equation 2.3.11 and 2.3.12 respectively show the calculated values of the

Inductor and Capacitor at 15 kHz frequency. The capacitor was selected to be at least 20%

greater than the calculated value to reduce any voltage ripple. The value of the inductor

selected was 100mH and the capacitor was 0.051 Figure 2.2.3 shows a schematic of the

DC-DC buck converter circuit and figure 2.2.4 the actual implementation in the excitation

system.

L =(

) = (

) = 99.88mH 100mH (2.3.11)

C =

=

= 0.051 (2.3.12)

14

Figure 2.2.3: DC-DC buck converter. [2]

Figure 2.2.4: DC-DC converter used in our project.

15

2.2.4 Simulation Results

The rectifier and buck converter shown in figure 2.2.5 was simulated in PSCAD. A firing

circuit design was included as the control of the IGBT. PWM had a duty cycle of 0.069

as shown in figure 2.2.6. Figure 2.2.7 shows that the rectified voltage was 350V DC

when the input was 208 and the output from the buck convertor was 25V.

Figure 2.2.5: Rectifier and buck converter simulated circuit.

Figure 2.2.6: IGBT firing circuit with 0.069 duty cycle.

16

Figure 2.2.7: Simulated graph of rectifier and buck converter design.

17

2.3 Design of Feedback Controller

Control system is a combination of individually distinct components working together to maintain

a desired system response [2]. There are two types of control systems: open loop and closed

loop. Open loop control system is shown in figure 2.3. The control system used in this project

was a closed loop system and is shown in figure 1.3.1. The closed loop system used negative

feedback to compare actual results with the desired results. The error was sent to the controller so

proper adjustments were made to produce the desired response [2].

Figure 2.3: Open Loop Gain

2.3.1 Measuring Elements for feedback control

Maximum voltage that could be injected into the microcontroller analog input pin was

5 . The maximum output of synchronous generator was 208 . In order to meet

microcontroller specification AC voltage needed to be converted to DC and stepped

down before being fed to the microcontroller. The following hardware was used to

accomplish this task:

Rectifier Transformer

Rectifier

Voltage Divider

Terminal voltage from the synchronous generator was fed into the primary side of the

rectifier transformer. Terminal voltage fed was from a single phase of the generator since

the load was balanced all phase had the same voltage. This voltage was stepped down

based on the transformer ratio. Equation 2.3.1 shows the relationship between the

primary voltage and the secondary voltage. Equation 2.3.2 shows the step down voltage

calculated assuming a transformer ratio of 20. A rectifier transformer was not found that

could achieve the calculated value. It was decided to purchase a rectifier transformer with

the highest transformer ratio. The output voltage of the rectifier was not purely

sinusoidal. The amount of clipping was acceptable error. Figure 2.3.1 shows the rectifier

Process Input Output

18

transformer that was chosen based on the data sheet it would step down the maximum

terminal voltage to 20 . The transformer turns ratio was approximately 10.

(2.3.1)

(2.3.2)

Secondary side of the transformer was connected to a rectifier so the ac voltage could be

converted into dc voltage. Another advantage of having the transformer was it provided

isolation from the synchronous generator.

H bridge rectifier in figure (2.2.1) was used to convert ac voltage to dc. Output voltage of

the rectifier was initially calculated based on the assumption that the input voltage would

be 20 . Equation 2.3.1 shows initial calculation along with the revised calculation

below based on the measured value of the secondary side of the transformer [1].

(2.3.3)

To ensure minimal fluctuation in dc signal being sent to the microcontroller the rectified

signal was passed through a 2μF capacitor. The measured output was higher than the

required specifications so voltage divider was implemented. The voltage divider in

figure 2.3.1 had a value of , 3.3 and .

Voltage divider was the last component of the hardware before the result was fed into the

microcontroller. The measured value from the voltage divider was 4.1 when the

voltage on the primary side of the measurement transformer was 208

19

Figure 2.3.1: Measuring Element.

2.3.2 PI Controller for Automatic Voltage Regulator

The main task of the PI controller is to reduce steady state error between the desired

response and the actual output [2]. The PI controller is a proportional plus integral

controller in Laplace form is shown in Equation 2.3.4. The proportional gain parameter

scales the initial error and the proportional integral keeps track of prior error so the

controller can send the appropriate output and the desired response can be met. In the

continuous time domain, the PI controller is represented using Equation 2.3.5. The

output of the PI controller is represented by the variable . The input is the

difference between the desired response and actual output.

(2.3.4)

(2.3.5)

In order to implement the PI controller in the microcontroller the continuous time domain

equation had to be changed into discrete form using difference equations. Equation 2.3.6

is the discrete form of the PI controller.

Measurement

Transformer

Rectifier

R1 R2

R4

R3

20

(2.3.6)

2.3.3 Selection of controller parameters

Root locus was mathematical model that was used to assist in determining PI controller

parameters. In order to plot the root locus each component of the control system required

appropriate transfer functions. The root locus of the simplified simulation model is shown

in figure 2.3.2. The initial response of the system is first order for a period of time before

becoming second order marginally stable. Figure 2.3.3 shows the root locus after

selecting the Kp = 0.0002 (proportional gain). The step response in figure 2.3.4 shows

that the system at steady state was stable with a settling time of 206 seconds with Ki =

0.019. The Kp and Ki determined in Matlab were starting values the PI controller in

PSCAD. Matlab code is provided in Appendix C

21

Figure 2.3.2: Root Locus of Simplified Simulation Model

Figure 2.3.3: Root Locus of Simplified Simulation Model with Kp= 0.0002

22

Figure 2.3.4: Step Response of Simulation Model with PI controller

2.3.4 Simulation results

Simplified model shown in figure 2.3.4 was simulated using PSCAD. The input to the model was

AC voltage which was rectified and fed to buck convertor the attached load was the same value

as field winding. The difference between the reference voltage and the load voltage was sent to

the PI controller in figure 2.3.5. The PI controller determined the amount of DC voltage that was

fed to the field winding. The initial values calculted in Matlab for the PI controller were used.

These values needed to be adjusted to correctly tune the PI controller. The final parameters of Kp

was 0.001 and Ki was 0.3 sec in PSCAD. Figure 2.3.6 shows the PI controller implemented in

PSCAD. The PI controller was tested by changing the reference voltage and ac input voltage.

Figure 2.3.8 shows the repsponse of the PI controller to the change in reference voltage. The

controller increases the amount of voltage being fed to the buck convertor until there error was

zero in steady state. Figure 2.3.9 shows the response of the PI controller to change in the ac input

voltage. The response was similar to change in the reference voltage.

23

Figure 2.3.5: Simplified Simulation Model

Figure 2.3.6: PWM firing Signal for IGBT in PSCAD

Figure 2.3.7: PI Controller Circuit

Buck converter 3-Φ Rectifier

Excitation Field winding (Load)

Feed to PI

controller

24

Figure 2.3.8: Settling time of PI controller

3 sec Settling

time

25

Figure 2.3.9: Response of PI controller while running converter.

Change in the

input AC

voltage

Change in the

reference

voltage needed

26

2.4 Design of Protection and Safety Features

2.4.1 Firing Circuit Isolation

The IGBT used was a voltage control device that required a gate voltage to set the

collector emitter conduction voltage. IGBT gate driver circuit was used which consisted

of a 5 V to 15 V DC to DC converter that was powered by the microcontroller. Opto-

coupler was used to isolate the microcontroller ground from the IGBT ground. BJT was

used to invert the signal and feed it to the gate driver mic5021 chip. This driver chip was

used to drive the IGBT. Figure 2.4.1 shows the complete schematic of the firing circuit

that was used.

Figure 2.4.1: Schematic diagram of the IGBT gate driver circuit

DC to DC converter:

DC to DC converter was used to provide power to the driver chip and also the opto-

coupler. This converter was powered from the microcontroller. The converter has an

internal isolation which isolated the controller ground from the power ground.

5 V 15 V

Optocouplers PWM signal

220 Ω 15

0

KΩ

1

KΩ

Microcontroller power

27

Opto-coupler chip:

Opto-coupler also called an Opto-isolator is an electronic device that conducted electrical

signals between two isolated circuits by using Infra-red light emitting diode. Opto-

coupler was used for high speed logic ground isolation. Opto-coupler prevented high

voltages from affecting the microcontroller.

MIC5021 chip:

The MIC5021 was used since it is a high speed high side MOSFET and IGBT driver

chip. This driver chip was designed to operate at high frequencies up to 100kHz. It is an

ideal choice for high speed switching application. Buck converter frequency was 15kHz

the MIC5021 was ideal for the convertor. Figure 2.4.1 shows the connection of the

MIC5021 which will turn the IGBT on and off. Figure 2.4.2 shows the behavior of the

firing circuit when PWM signal was provided by the microcontroller.

Figure 2.4.2-PWM signal from the Microcontroller and MIC5021

PWM signal

sent from the

Microcontroller

PWM signal

sent from the

MIC5021 to

IGBT

28

2.4.2 Generator Protection

Generator protection was needed to prevent excessive current to the field winding.

Circuit breakers were going to be used but the cost of circuit breakers was not within the

budget. Fuses were used, these are electric devices that have a low resistance value that

act as a line of defence to provide overcurrent protection. These devices consist of a

metal wire or strip that break or melts whenever high current flows through it. The fuse is

rated for 1A.

2.4.3 Thermal Protection of IGBT's - Heat Sink Design

Switching devices such as IGBTs and MOSFETs dissipate heat during operation due to

switching power loss. The increase in power dissipation from such microelectronic

devices increase the heat dissipation and may cause internal damage. Thermal

management becomes an important part of electronic product design. Controlling the heat

dissipation of the IGBT improves the performance reliability and life expectancy of the

device.

Heat sinks are used with high power components to enhance heat dissipation to a lower

ambient temperature (air). Heat sinks maintain device temperature by increasing surface

area for better management of generated heat.

Different types of heat sinks are available such as stampings, extrusions, bonded or

fabricated, castings, and folded fins heat sinks. Each type is used for a specific power

level and the needed heat dissipation. In our design we chose the stampings heat sinks

which is usually made from a copper or aluminum sheet as a coolant agent. This type is

suitable for high volume production and advanced devices with high frequency operation.

Heat Sink Selection:

To correctly select the heat sink consider the thermal circuit in figure 2.4.3.

29

Figure 2.4.3: Thermal Resistance Circuit [REFERENCE]

The heat sink thermal resistance was calculated. The datasheet of the IGBT was used to

find the maximum junction temperature Tj and the thermal junction to case resistance RΦj-

c and thermal junction to ambient resistance RΦj-A [14].

(2.4.1)

(2.4.2)

(2.4.3)

Where: Tj is the maximum junction temperature.

Tc is the temperature of the case.

TH is the heat sink temperature.

TA is the coolant temperature or the ambient temperature which is between 23 to

25 C room temperature.

RΦc-H is the thermal case to heat sink resistance which is ignored as it is

insignificant and it will not affect the calculation.

RΦH-A is the thermal heat sink to ambient resistance.

Pd is the maximum power dissipation of the device.

RΦH-A

RΦC-H

RΦj-c

30

Equation 2.4.4 was used to calculate the total junction to ambient resistance:

(2.4.4)

From the equation 2.2.4 the thermal heat sink to ambient resistance RΦH-A was found.

(2.4.5)

From the IGBT datasheet: Tj = 150 C, Pd = 179 w, RΦj-c = 0.7 C/w, and RΦj-A = 40 C/w.

We will choose TA to be 23 C.

Hence,

C/w.

Therefore, the maximum thermal heat sink to ambient resistance needed is 0.0095 C/w.

To find the size of the aluminum we have to use [15]

(2.4.6)

The thermal conductivity of Al is 205 w/ m K that is (2.05 w/cm C). RΦH-A is equal to

0.0095C/w. The thickness of the aluminum plate used is 0.125 in (0.3175 cm) and the

height is 2.5 in (6.35 cm).

(2.4.7)

Therefore, the minimum size of heat sink needed was:

t = 0.125 inch, L = 1.0079 inch, and h = 2.5 inch see figure 2.2.4.

31

Figure 2.4.4: Heat sink

In the actual design we used a heat sink with a bigger size to ensure that the heat sink

does not overheat with dimension (t = 0.125 inch, L = 3 inch, and h = 2.5 inch).

The thermal resistance of this heat sink was:

(2.4.8)

2.4 Design of Start-up Power Supply

Batteries are needed in our design to initially supply the field winding with current. During start-

up two 12V batteries in series supply the field winding current momentarily until a double pole

double throw relay switches the battery path from supplying the windings to being supplied by

the charger as seen in figures 2.4.2 and 2.4.3. In addition to the battery supplying the rotor field

winding, the battery must also supply the relay coil with 24V. Relay power must always be

supplied however, supply to the field winding and battery charger must be interchanged as the

battery can't supply the needed current while being charged. The battery is only supplying the

relay with power, whereas the relay is controlled by a darlington circuit and an Arduino

microcomputer. Shown in figure 2.4.1 is the control circuit of the DPDT relay. The darlington

chip contains seven channels allowing low power output devices such as the microcontroller to

drive high current devices such as the relay switch. The optocoupler connected to the 5V-5V DC-

1.0079 inch

2.5 inch

0.125 inch

32

DC converter is used to provide isolation between the controller ground and the power switch

ground.

It was determined two 12V batteries in series, 24V, would be a sufficient amount to achieve the

aforementioned tasks. At 24V from the batteries, the field winding current is about 0.3A and line

to line voltage is about 100V. The batteries combined voltage was 25.1V. The batteries we used

were VRLA gel encapsulated with nominal cell voltages of approximately 2.1V on average,

resulting in the 12 cells we used actually having voltages of approximately 2.1V obtained by

dividing 25.1V by 12 [8]. These values were measured using LabVolt software and are acceptable

as both field current and line-to-line voltage requirements are satisfied with Vl-l > 80V, and field

current < 0.9A. Therefore, to get the needed field current and to power the relays two batteries

were needed in the design.

1. Generator DC field

2. Output of buck

converter

3. Battery

1 KΩ

Microcontroller

signal

1 2

3

+ -

24 V

Field Winding

Battery Charger

Batteries

Open circuit

Generator

Figure 2.4.6: Normally closed position of relay

Figure 2.4.5: Controlling circuit of DPDT relay.

33

Having two 12V batteries running constantly requires them to be coupled to a battery charger as

well to ensure the batteries stay at operating capacity. After the initial start up, the battery no

longer feeds current to the field winding. At this point the generator terminal voltage begins to

power the field winding and the battery is no longer needed for supply. The battery is then

toggled to be charged by the charging circuit which is initially disconnected. The charging circuit

charges the battery as the battery supplies the relay coils until next use of the machine. The

charging circuit is supplied by rectifying and stepping down the ac mains to feed to the input side.

Theory concerning batteries and the charging circuit, how hardware components were chosen and

mounted, and basic knowledge of how the circuit works and was tested will be discussed.

2.4.1 Selection of Battery

As little was known about batteries prior to their use in this project, research concerning many

types was facilitated. A comparison regarding battery capacity, memory, and general use was

needed to be done to choose what type of battery to use, contrasting between NiCd, NiMH, Li-

ion, and lead acid/SLA/VRLA batteries. NiCd and NiMH batteries exhibit the memory effect

resulting in less charge held over time unless periodically recharged and used. NiCd batteries also

have high discharge rates and are made of more toxic materials and are expensive. NiMH

batteries are less environmentally damaging than NiCd and even less prone to memory effects,

although they still have are higher maintenance regarding charging, have high discharge rates, are

more expensive than NiCd, and generally used for laptops and mobile devices. Lithium ion

batteries weren't considered as they are very expensive and require a protection circuit.

Consequently, we chose SLA batteries instead of other batteries for various reasons [9]. They are

low maintenance, have no memory effect, capable of high current pulses (>1C, where C is the

battery Amp-hour rating), high voltage per cell, low cost, and safer than lead acid as the liquid

inside is in a gel form. Referring to figure 2.4.4, two 12V, 7.2Ah, SLA batteries were purchased

and placed in series with a diode soldered to leads between them for protection against accidental

reverse connection. The batteries were measured with readings of 12.6V, and 12.5V, combining

to 25.1V.

Open circuit

Field Winding

Battery Charger

Batteries

Generator

Figure 2.4.7: Relay position during start-up transience of generator.

34

2.4.2 Battery Charger

A charging circuit to accommodate for the two batteries was designed and tested with all

calculated values. The design is centered around the IC L200CV adjustable voltage and current

regulator [10]. The entire charger design is adapted from a general circuit provided in the L200

Figure 2.4.8: 2 12V SLA batteries with a high voltage diode between them.

35

datasheet application note figure shown below in figure 2.4.6.

Figure 2.4.9: Pin labelled drawing of L200C voltage/current regulator.

The L200 is an adjustable voltage and current regulator, with a 2A max output current. According

to figure 2.4.5 it has 5 pins. Pin 1 is input and pin 5 is output. Pin 2 has the function of detecting

the potential between pins 5 and 2, Vlim, and ultimately limits the output current I0. Vlim=0.45V,

and if it is >0.45V then too much current has outputted and could damage the IC. Pin 4 is the IC

voltage Vref,l200 which is basically voltage between pin 4 and pin 3, and is equal to 2.77V. As long

as output current is less than the maximum 2A the L200 sets pin 4 to 2.77V. However, if output

current is greater than the maximum rated current then pin 5 (V0) is dropped to keep I0 in bounds.

In this way the L200 serves as the heart of the battery charger.

Figure 2.4.10: Battery charger circuit.

36

The circuit in figure 2.4.7 is the battery charger circuit that is designed and mounted on the

perforated board along with the rest of our circuits. The 5 pin L200CV chip is the heart of the

operation. The circuit consists of: two smoothing capacitors; the L200 IC with input on pin 1 and

output on pin 5; three resistors with various functions that will be mentioned, two diodes (for

protection); and ultimately an 32V AC/DC adapter on the input and wires connecting to battery

leads on the output. Referring to component labeled circuit figure 2.4.8 below, the two capacitors

on the input and output that are in a low-pass configuration (Tf=(jωRC+1)-1

) were chosen with

general values serving only the purpose of cleaning up higher frequency components such as

spikes and ripples that could damage the battery or circuit. Since the operating frequency is 60Hz

(coming from the wall), and the capacitors are very small at C1=220nF and C2=100nF, a high

reactance (Xc=(ωC)-1

) is achieved at high frequencies blocking out harmonics and resulting in a

clean DC output. Rp serves the purpose of protecting the IC in-case the battery is connected in

reverse. A maximum 100mA of reverse current is allowed and Rp=270Ω is designed to allow a

maximum of approximately 90mA. Rsc serves as the charging current control. Trickle or slow

charge battery charging rates are generally around C/10 where C is the battery's Amp-hour rating.

Rsc=0.5Ω is set for trickle charge at I0=900mA [11]. R1 and R2 are derived from the output

voltage, which in our case is comprised of 12 cells at approximately 2.1V each, totalling to

roughly 25.1V. However, anything less than 2.15V per cell will not charge the lead acid cells at

all. 2.3V per cell charging voltage was chosen to charge to a float voltage allowing for long

battery life and less water loss [12]. R1 is chosen as 1kΩ to limit the current across pin 4 and

ground. R2 is generally a potentiometer as this way a variable output voltage is attained and

charging of different battery capacities is possible however, this is not needed in our case.

R2=10kΩ is found considering an output voltage of approximately 27.5V and by applying nodal

analysis at pin 4 (Vref,l200). Finally, the diodes were selected as high powered diodes to allow for

high amounts of current to protect against battery back discharge. The SBYV-28-200 diode was

selected [13]. The equations and methods of finding these values is discussed next.

37

Figure 2.4.11: Nodal analysis at the labelled node yields shown equation. A variable resistance would account for a

variable voltage charger.

Referring to the above labeled circuit figure, capacitors C1 and C2 were chosen such that gain at

60Hz is unity and at high frequencies is small. Taking the 100nF capacitor and ignoring the R

term for estimation purposes:

(2.4.1)

Rp is a pull-down resistor serving to protect the IC from reverse battery connection. The IC can

have a maximum of 100mA entering ground pin 3, and thus is designed around this limitation.

Pin 3 to ground shares the voltage drop of the battery and thus we design for a current of 90mA

and obtain the required resistance:

(2.4.2)

Since Rp had current around 90mA a 0.25W resistor will burn. We chose to use 10W ceramic

resistors to overcome this problem as Rp takes up I2R=(0.09A)

2(270Ω)=1.7W of power on paper.

When measured V2/R=(25.1V)

2/270Ω=2.3W. Therefore a higher power resistor must be used.

R1 was chosen so that the current in the pin 4 IC branch was

low. Since the voltage Vref on pin 4 (to gnd.) is 2.77Ω,

R1=1kΩ was a sufficient choice to limit current. R2 is chosen

Figure 2.4.12: High power resistor.

38

such that 2.3V can appear across each of the 12 cells in charging which corresponds to about

27.5V total.

Referring to pin 4 of the labelled schematic, nodal analysis yields:

(2.4.3)

(2.4.4)

Rsc determines the initial charging current which flows from the output (pin 5). L200C has a max

current capability of 2A. Generally for trickle charge this is set to about 0.1C, where C=7.2Ahr.

We chose this to be about 0.125C for a little more than slow charging current but still nowhere

near quick charging. At 0.125C we need 0.9A, and since voltage drop Vlim between pins 5 and 2

is 0.45V we have:

(2.4.5)

Finally, taking into account the power lost in the IC:

(2.4.6)

A heat sink is definitely needed with that amount of power.

Referring to figure 2.4.10, the components that had been picked out consisted of ceramic

capacitors, a larger wire type resistor for 0.5Ω, two 10W ceramic resistors to equal 270Ω, two

diodes and the L200 IC. The IC received a heat sink and was to be screwed in place. The circuit

was assembled on a perforated board and each component soldered in place. The AC/DC adapter

was attached finally and the circuit was ready to be tested. Referring to figure 2.4.11, it is seen

that the output voltage of the charging circuit is above the battery voltage and therefore charging

is being done.

39

Figure 2.4.13: Completed battery recharging station.

Figure 2.4.14: Demonstrating that the output of the charger is charging the battery by showing on the multimeter a

voltage higher than that of the battery's.

40

Chapter 3 Design of a Digital Control System

A Microcontroller was needed to implement a digital PI controller and control switching

from battery to the static exciter. Analog PI controller would have needed hardware to be

changed and an amplifier to amplify the error. Manually switching from battery to static

exciter would have produced inconsistent results due to different switching time. The use

of a microcontroller allowed for a self-regulating system. The AVR was implemented in

the microcontroller. Upon initial start-up of the system the microcontroller was

responsible for switching from the battery to the static exciter. The error between the

reference voltage and RMS were sent to the PI controller. The controller adjusted the duty

cycle of the PWM.

3.1 Functions and Requirements of the Digital Controller

The following key attributes considered in selection of the microcontroller:

Pulse Width Modulation implemented in hardware

Minimum of Five Analog to Digital Convertor Channels

Readily available libraries and coding examples

Minimum 10 digital input/output Channels

The speed of the microcontroller was considered, but since the system frequency is 60 Hz

this was not a key requirement. The microcontroller needed to be fast enough to perform

all required tasks.

3.2 Factors Considered in Selection of Microcontroller

Based on these key attributes the Arduino Uno was chosen. Arduino Uno uses the

ATmega328P processor [3]. The Arduino Uno has a 32KB flash memory, 14 digital

input/output pins, 6 pulse width modulation pins and six analog pins. The resolution of

the analog to digital convertor was 10 bits. Arduino clock speed was 16 MHz which was

fast enough to perform all required tasks. There are large numbers of libraries available

on the internet including libraries for LCD display, A/D conversion, and PWM. Arduino

uses the programming language Processing which is based on C. Figure 3.1 shows a

picture of the microcontroller selected.

41

Figure 2.2: Arduino Uno

3.3 Peripheral Hardware

An important input into the microcontroller is the reference voltage. This voltage was

compared with terminal voltage to produce the correct PWM signal. Initially reference

voltage was set at 100 . Potentiometer was implemented so a user could change the

voltage to a value between 50 to 190 . Turning the potentiometer clockwise will

increase the reference voltage by increments of 10 and counterclockwise will equally

decrement the voltage.

An LCD was attached to the Arduino that displayed reference voltage, terminal voltage

and generator current [4]. The LCD required 7 digital I/O pins, it has two-line display

with 16 characters per line. Reference voltage was displayed on the first line and

terminal voltage along with generator current on the second line.

42

Figure 3.3: LCD

3.4 Analog to Digital Conversion

The terminal voltage from the generator was a continuous signal. The microcontroller

can only read discrete signals. The 10-bit resolution in Arduino quantized the continuous

signal into discrete to be read. To ensure the continuous signal was properly

reconstructed into a discrete signal the appropriate sampling frequency ( was chosen.

Recommended theoretical sampling frequency should be greater than the Nyquist rate

calculated in Equation 3.4.1 [5]. For practical purposes the recommended sampling

frequency should be at least thirty times the Nyquist frequency. Equation 3.4.2 shows that

the calculated sampling frequency should be at least . The Arduino was set to

sample at , which met the minimum requirement.

(3.4.1)

(3.4.2)

The performance of A/D converter can be measured by mean square error also known as average

distortion [6]. Equation 3.4.3 shows the average distortion of the A/D convertor.

(3.4.3)

43

3.5 Digital to Analog Conversion

The DAC converts a discrete signal into analog signal. The DAC in Arduino has an 8-

bit resolution which produces a PWM signal that was outputted to the system [7]. The

square wave is constructed by sending high and low signals for a distinct period of time.

The timer counts up to 255 until the duty cycle is reached. For example, if a 50% PWM is

needed it keeps the signal high till it reaches 128 and then low for the remaining count.

The frequency of the DAC needed to be set according the switching frequency of buck

convertor. The switching frequency of the buck convertor was . In order to

achieve this clock select bit was set to 010 so the pre-scalar was 8. Waveform generation

bits are set to 111 for fast PWM with OCRA controlling the top limit of 128. Equation

3.5.1 shows how the 15 frequency was calculated. The calculation of the mean

square error due to changing the timer count can be found in appendix C.

(3.5.1)

44

Chapter 4 Design of Control Software Program

Figure 4.1 shows a flowchart of the program implemented in Arduino. The five components are:

System Initialization, Switching, Updating Reference Voltage, PI Controller and Updating LCD.

Full Arduino UNO code is available in Appendix E.

Figure 3.1: Main Flowchart.

4.1 System Initialization

In this section the pins were assigned for hardware and variables used in coding were

defined. PWM signal is being outputted from Pin 5 of the Arduino. Digital pins

2,3,4,10,11 and 12 are being uses for the LCD [4]. The Relay_Pin was defined as pin 7.

System Initialization

Updating LCD

PI Controller

Updating Reference

Voltage

Switching

45

Analog pin A0 was used to read the measurement of the terminal voltage and pin A3 to

change the reference voltage.

4.2 Switching

The switching flowchart in Figure 4.2 shows the code for this part of the program.

Before the start of the loop, Battery was initialized to true. Setting Pin 7 the Relay_Pin

high (5V) and true sent a signal to the relay to connect the battery to the field winding

and a low (0V) signal to the relay connects the static exciter to field winding. The

microcontroller is writing the high signal as long as the battery is equal to true. After 5

seconds the Battery is equal to false and the Relay_Pin is a low signal.

Figure 4.2: Switching Flowchart

Battery ==

true?

Relay_Pin = 1

t >= Battery

Time?

Battery = False

Relay_Pin = 0

End

Yes

No

No

Yes

Start

46

4.3 Updating Reference Voltage/LCD

After the battery is disconnected from the system, a change in reference voltage is read from

the analog pin A3. Turning potentiometer changes the reference voltage. The program

will check the analog pin every 10 samples to update the reference voltage. LCD is

updated every 1000 samples to display the current terminal line to line voltage and the

line to line reference voltage.

4.4 PI Controller

The input into the PI controller was the error between the terminal voltage and the

reference voltage. The user has the option of choosing the desired reference voltage in

terms of line to line voltage. The line to line voltage was divided by a factor of 46 so it

can be compared with the terminal RMS (root mean square) voltage and was defined as

Vref. Analog pin A0 reads the terminal RMS voltage from the final component of the

measuring element. The microcontroller quantizes this values and assigns a number

between 0 – 1023. In order to compare this value with the desired reference voltage the

quantized value was scaled by dividing by 1023 and multiplying by 5V. This value was

defined as Vin, and the error sent to the PI controller was the difference between Vref

and Vin. Equation 2.3.6 was used and the following changes were made to the variables:

current output of the controller was defined as y, prior output as y1, current input as x and

prior input as x1. Equation 4.4 shows the implementation of the PI controller in

software. Initially all values were set to zero. The minimum value of y was set to 0 and

the maximum value of y was set to 4.1. The maximum and minimum values were set as

safeguards to ensure that the output would never become negative or exceed the

maximum RMS value. The output of y is divided by 4.1 and then multiplied by the

PWM_MAX_COUNT, which represents the PWM counter limit stored in OCRA. This

calculation gives the correct duty cycle to be sent to the system. The PI controller

flowchart is shown in figure 4.4

(4.1)

47

Figure 4.4: PI Controller

Start

val = analogRead(A0)

= val*5/1023

x1 = x

y1 = y

y<0?

y>Max_Voltage?

y = 0

y = Max_Voltage

pwm_val = y*(PWM_MAX_COUNT/MAX_VOLTAGE

analogWrite(PWM_PIN,pwm_val)

End

Yes

es

Yes

No

No

48

Chapter 5 Fabrication and Testing

The PI controller was tested using the Kp and Ki values that were determined in PSCAD.

With these values the system went unstable. Rated load was attached to the generator

terminal and the PI controller was tuned manually by changing the values of Kp and Ki in

software. The strategy used was to have a small values for both Kp and Ki and observe

the response. The values initially found were 0.3 for Kp = 0.3 and 0.1 for Ki. The

response of the system to change in reference voltage was measured to be approximately

45 seconds with an absolute error of less than 5% in the range of 50 to 190 . As

settling time was longer than what was desired, the Ki parameter was increased to 0.8 and

the settling time decreased.

Initially when the generator was turned on the field winding was excited from two 12V

batteries. After 5 seconds the batteries were disconnected from the field winding and the

static exciter was connected to provide DC power to the field winding. When reference

voltage was set at 100 it took the excitation system approximately 5 seconds to build

up the voltage to 100 . Figure 5.1 shows the response of the excitation system during

initial start-up of the generator. In the far right corner the change in time being measured

between the two cursors was shown, and it can be seen steady was reached in 5 seconds.

The response being measured was the change in RMS value from the measuring element.

Figure 3.3 shows the value of the reference voltage and terminal voltage it can be seen

that the error was within the 5%.

Figure 5.1: Controller behavior for start-up of generator.

49

The second test performed was measuring the step response of the excitation system as

the reference voltage was changed from 100 to 190 . Figure 5.2 shows that the

excitation system takes 4.2 seconds to reach steady state. The oscilloscope measured the

change in the RMS. Figure 5.3 displays the actual reference voltage and terminal voltage

outputted from the microcontroller. The error between the terminal voltage and reference

voltage was within the 5% proposed.

Figure 5.2: Step Response of excitation system to change in reference from 100 to 190 .

Figure 5.3: LCD displaying Vref and Vt.

The third test performed was reducing the reference voltage from 190 to 100 .

Settling time of the excitation system increase to 10.70 seconds. Figure 5.4 shows that

50

the RMS value initially overshoots the steady state value before becoming steady. Figure

5.5 shows that the error between the reference voltage and terminal voltage fell within the

5% range.

Figure 5.4: Step Response of excitation system to change in reference from 190 to 100 .

Figure 5.5: LCD displaying Vref and Vt.

The last change in reference test was performed by changing the reference voltage from 100

to 50 . Excitation response was similar to the response when the voltage was changed

from 190 to 100 . Figure 5.6 shows the response with a settling time of 10.70

seconds and figure 5.7 shows that the error between the two voltages was within the 5%

margin.

51

Figure 5.6: Step Response of excitation system to change in reference from 100 to 50

Figure 5.7: LCD displaying Vref and Vt.

Response of the excitation system was measured when a three phase Y-connected 10mH

inductive load in series with 60Ω resistive load was attached. Figure 5.8 shows that there

was sudden drop in the RMS voltage when the load is connected. The excitation system

reached steady state in 2.8 seconds. Though a picture of the LCD showing the reference

voltage and terminal voltage is not available, the error fell within the 5% range.

52

Figure 5.8: Response of the excitation system with addition of an inductive load.

Figure 5.9 shows the response of a three phase Y-connected 10 µF capacitive load.

Similar to the inductive load there was a sudden increase in line voltage when the load

was connected. The excitation system was able to get steady state in 4.4 seconds. Though

a picture of the LCD showing the reference voltage and terminal voltage is not available,

the error fell within the 5% range.

Figure 5.9: Response of the excitation system with addition of a capacitive load.

53

Chapter 6 Conclusion

An excitation system was successfully designed, built and implemented to feed the field winding

DC current and regulate the terminal voltage of the 1.5 KVA, 60Hz, 208V, 3- phase synchronous

generator. Automatic voltage regulator maintained the steady state error of the generator terminal

voltage within ±3 % of the reference voltage for a specified voltages between 50 to 190 .

The error range achieved was better than the proposed value of ±5%. The excitation system had

the ability to provide 1.25A DC to the field winding but this value exceeded the recommended

field current. The battery charger successfully recharged the two 12V batteries used for initial

excitation. Upon initial start up the generator takes approximately 5 seconds to build voltage of

the generator up to the reference voltage. The excitation system took 4.2 seconds to reach

steady state when the reference voltage was increased from 100 to 190 . It took

10.70 seconds to reach steady state when the reference voltage was decreased from

100 to 190 .

54

Bibliography

[1] D.W.Hart, Power Electronics, New York: McGraw-Hill, 2011.

[2] R. D. a. R. H. Bishop, Modern Control Systems, New Jersey: Pearson Hall, 2011.

[3] Atmel, "www.sparkfun.com," Atmel Corporation, 01 Febuary 2009. [Online]. Available:

https://www.sparkfun.com/datasheets/Components/SMD/ATMega328.pdf. [Accessed 10

10 2015].

[4] Arduino, "www.arduino.cc," arduino.cc, 17 August 2015. [Online]. Available:

https://www.arduino.cc/en/Tutorial/LiquidCrystalDisplay. [Accessed 15 January 2016].

[5] B. Lathi, Linear Systems and Signals, New York: Oxford University Press, 2005.

[6] J. D. Powell, G. F. Franklin and M. L. Workman, Digital Control of Dynamic Systems, Half

Moon Bay: Ellis-Kagle Press, 1998.

[7] K. Shirriff, "www.arduino.cc," arduino, 1 July 2009. [Online]. Available:

htttps://www.arduino.cc/en/Tutorial/SecrectsOfArduinoPWM. [Accessed 1 July 2015].

[8] I. Cowie, "All Abot Batteries Part 3: Lead-acid Batteries," 13 January 2014. [Online].

Available: http://www.eetimes.com/author.asp?section_id=36&doc_id=1320644.

[Accessed 6 January 2016].

[9] "Whats the Best Battery?," Battery University, 11 January 2011. [Online]. Available:

http://www.batterycharger.com/learn/article/whats_the_best_battery. [Accessed 8

January 2016].

[10] STMicroelectronics, "L200," January 2000. [Online]. Available:

http://www.zen22142.zen.co.uk/Circuits/Power/l200.pdf. [Accessed 2 January 2016].

[11] W. C. Ltd., "Battery Chargers and Charging Methods," 2005. [Online]. Available:

http://www.mpoweruk.com/chargers.htm. [Accessed 11 January 2016].

[12] P. Technology, "Lead Acid Battery Charging Basics and Chargers," 23 November 2015.

55

[Online]. Available: http://www.powerstream.com/SLA.htm. [Accessed 6 January 2016].

[13] Vishay, "Soft Recovery Ultrafast Plastic Rectifier," 10 February 2015. [Online]. Available:

http://www.vishay.com/docs/88737/sbyv28.pdf. [Accessed 3 February 2016].

[14] S. Lee, "AAVID THERMALLOY," [Online]. Available:

http://www.aavid.com/sites/default/files/technical/papers/how-to-select-heatsink.pdf.

[Accessed 18 February 2016].

[15] A. A. Ali, "Heat Transfer Lectures - Conduction," [Online]. Available:

http://www.scribd.com/doc/22016082/Heat-transfer-lectures-1-conduction#scribd..

[Accessed 19 February 2016].

[16] Guru,Hiziroglu, Electric Machinery and Transformers 3rd ed., New York: Oxford University

Press, Inc., 2001

56

Appendix A

DC field winding calculation to find its parameters:

Input step DC voltage is 20 volts.

Output measured current steady state is 0.25 A.

The slope of the line measured using figure … is 359.4

For first order response:

V(t) at t = 0 sec;

Inductor voltage is

Buck Converter Inductor and Capacitor Selection:

57

1- Best Scenario Case:

Output voltage of the synchronous generator: 208 V

Vphase =

= 120 V

Voltage after the Diode rectifier:

The best case is when we have 0.9 A at the output of the buck regulator so the voltage

will be

=

=

= 0.259

Inductor Selection:

Lmin =

=

= 30.01 mH , where is the switching frequency.

IL = IR =

=

= 0.9 A

Imax = IL +

, = 5% A

Imax = 0.9 A +

= 0.9225 A

Imin = IL -

= 0.8775 A

L =(

) = (

) = 1.196 H

The inductor must be rated for rms current,

IL, rms =

=

= 0.9 A

The inductor voltage when the switch is closed is = 280.8 – 72.9 = 207.9 V

The inductor voltage when the switch is open is = 72.9 V

Capacitor Selection:

Voltage ripples is

, Let’s choose it to be 10 %

58

C =

=

= 0.7744

The capacitor must be rated for the 72.9 V output.

Worst scenario Case-1:

Let’s choose the output of the buck regulator to be 25 V

Output voltage of the synchronous generator: 85 V

Vphase =

= 49.07 V

Voltage after the Diode rectifier:

=

=

= 0.635

Inductor Selection:

Lmin =

=

= 14.78 mH , where is the switching frequency.

IL = IR =

=

= 0.9 A

Imax = IL +

, = 5% A

Imax = 0.9 A +

= 0.9225 A

Imin = IL -

= 0.8775 A

L =(

) = (

) = 0.591 H

The inductor must be rated for rms current,

IL, rms =

=

= 0.9 A

The inductor voltage when the switch is closed is = – = 41.9 V

The inductor voltage when the switch is open is = V

Capacitor Selection:

59

Voltage ripples is

, Let’s choose it to be 10 %

C =

=

= 0.772

The capacitor must be rated for the V output.

3- scenario Case:

Output voltage of the synchronous generator: 260 V

Vphase =

= 150 V

Voltage after the Diode rectifier:

The best case is when we have 0.9 A at the output of the buck regulator so the voltage

will be

=

=

= 0.069

Inductor Selection:

Lmin =

=

= 37.70 mH , where is the switching frequency.

IL = IR =

=

= 0.3 A

Imax = IL +

, = 5% A

Imax = 0.3 A +

= 0.3075 A

Imin = IL -

= 0.2925 A

L =(

) = (

) = 1.49 H

The inductor must be rated for rms current,

IL, rms =

=

= 0.3 A

60

The inductor voltage when the switch is closed is = 350 – = 325.7 V

The inductor voltage when the switch is open is = V

Capacitor Selection:

Voltage ripples is

, Let’s choose it to be 10 %

C =

=

= 0.781

The capacitor must be rated for the 24.3 V output.

With :

L =(

) = (

) = 149.8 mH 150 mH

C =

=

= 0.0776

_____________________________________________________________________________

With :

L =(

) = (

) = 119.8 mH 120 mH

C =

=

= 0.062

_____________________________________________________________________________

With :

L =(

) = (

) = 99.88 mH 100 mH

C =

=

= 0.051

61

Appendix B

Open Circuit Test Short Circuit Test

If V_LL If Ia

0.009 4.5 0.006 0.143

0.1 27.8 0.024 0.25

0.2 55.8 0.032 0.295

0.3 84 0.1 0.769

0.4 111.3 0.154 1.071

0.5 135.6 0.211 1.476

0.6 158.4 0.255 1.723

0.7 179.6 0.311 2.083

0.8 198.3 0.358 2.386

0.855 206.5 0.401 2.671

0.456 3.024

0.496 3.198

0.53 3.308

Table 2: Open and short circuit test results.

Calculating the Saturated and Unsaturated Xs

If

[Amp]

Saturated

Line

voltage

Saturated

Phase

voltage

Unsa-

turated

Line

Voltage

Unsaturated

phase

Voltage

Line

current

Ia

[Amp]

Saturated

Armature

Reactance

(Xs)

pu Unsaturated

Armature

Reactance

(Xs)

0 4.5 2.59807 4.5 2.59807 0.1253 20.7256 0.71864 20.72567401

0.075 19 10.9696 19 10.9696 0.59249 18.5042 0.64161 18.50422575

0.15 41 23.6713 41 23.6713 1.05968 22.3297 0.77426 22.32970285

0.225 62 35.7957 62 35.7957 1.52687 23.4357 0.81261 23.43574177

0.3 84 48.4974 84 48.4974 1.99406 24.3131 0.84303 24.31312535

0.375 102 58.8897 102 58.8897 2.46125 23.9188 0.82936 23.91880767

0.45 123 71.0140 123 71.0140 2.92844 24.2419 0.8405 24.24195748

0.525 141 81.4063 145.95 84.2642 3.39563 23.9659 0.83099 24.80784129

0.6 158.4 91.4522 166.8 96.302 3.86282 23.6669 0.8206 24.92286972

0.675 175 101.036 187.65 108.33 4.33001 23.3258 0.8088 25.01307574

0.75 190 109.696 208.5 120.377 4.7972 22.8584 0.79259 25.08571165

62

0.825 202 116.624 229.35 132.415 5.26439 22.1449 0.76785 25.14545526

Table 3: Calculating saturated and unsaturated armature reactance.

Load Test

Load

R

V_LL

[volt]

I_L

[Amp]

If

[Amp]

20 149.7 3.55 0.843

24 161.3 3.43 0.843

30 173 3.215 0.843

34 179.4 3.01 0.84

40 184.2 3.658 0.84

48 188.8 2.274 0.838

60 192.8 1.86 0.838

80 196 1.419 0.835

120 198.2 0.958 0.83

240 200.4 0.486 0.829

255 205.1 0.465 0.858

375 205 0.317 0.854

Table 4: Load test results.

63

Load Angle characteristics

Line

Voltages

[Volt]

Line

currents

[Amp]

Power [W] Angle δ

[rad]

Angle δ

[deg]

149.7 3.55 920.47242 0.7380850 42.310606

161.3 3.43 958.27269 0.6842022 39.221786

173 3.215 963.35799 0.6192688 35.499486

179.4 3.01 935.29704 0.571825 32.779809

188.8 2.274 743.62345 0.4327731 24.808650

192.8 1.86 621.1272 0.3544102 20.316512

196 1.419 481.72489 0.2708667 15.527395

198.2 0.958 328.87418 0.1833137 10.508430

200.4 0.486 168.69204 0.092752 5.3170383

205.1 0.465 165.18828 0.08674 4.9725057

205 0.317 112.55732 0.0592424 3.3960656

Table 5: Load angle calculations.

Figure A.2.1: Load Angle Characteristics Curve for the Synchronous Generator.

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Rea

l Po

wer

P [

W]

Load angle δ [rad]

Load angle characteristics curve

Angle δ [rad]

64

Appendix C

Table 6: Error in PWM signal.

PWM

MAX

COUNT

DUTY

DESIRE

D

PWM

DESI-

RED

PWM

ACHIEVA-

BLE

DUTY

ACTUA

L

ERR

OR

MEAN

SQUARE

ERROR

128 0.01 1.28 1 0.007812

5

0.047

85156

0.001886708

0.02 2.56 2 0.015625 0.047

85156

0.03 3.84 3 0.023437

5

0.047

85156

0.04 5.12 5 0.039062

5

0.000

54932

0.05 6.4 6 0.046875 0.003

90625

0.06 7.68 7 0.054687

5

0.007

83963

0.07 8.96 8 0.0625 0.011

47959

0.08 10.24 10 0.078125 0.000

54932

0.09 11.52 11 0.085937

5

0.002

03752

0.1 12.8 12 0.09375 0.003

90625

0.11 14.08 14 0.109375 3.228

3E-05

0.12 15.36 15 0.117187

5

0.000

54932

65

0.13 16.64 16 0.125 0.001

47929

0.14 17.92 17 0.132812

5

0.002

63572

0.15 19.2 19 0.148437

5

0.000

10851

0.16 20.48 20 0.15625 0.000

54932

0.17 21.76 21 0.164062

5

0.001

21986

0.18 23.04 23 0.179687

5

3.014

1E-06

0.19 24.32 24 0.1875 0.000

17313

0.2 25.6 25 0.195312

5

0.000

54932

0.21 26.88 26 0.203125 0.001

07178

0.22 28.16 28 0.21875 3.228

3E-05

0.23 29.44 29 0.226562

5

0.000

22337

0.24 30.72 30 0.234375 0.000

54932

0.25 32 32 0.25 4.930

4E-32

0.26 33.28 33 0.257812

5

7.078

6E-05

0.27 34.56 34 0.265625 0.000

26256

0.28 35.84 35 0.273437

5

0.000

54932

66

0.29 37.12 37 0.289062

5

1.045

1E-05

0.3 38.4 38 0.296875 0.000

10851

0.31 39.68 39 0.304687

5

0.000

29368

0.32 40.96 40 0.3125 0.000

54932

0.33 42.24 42 0.328125 3.228

3E-05

0.34 43.52 43 0.335937

5

0.000

14277

0.35 44.8 44 0.34375 0.000

31888

0.36 46.08 46 0.359375 3.014

1E-06

0.37 47.36 47 0.367187

5

5.778

1E-05

0.38 48.64 48 0.375 0.000

17313

0.39 49.92 49 0.382812

5

0.000

33965

0.4 51.2 51 0.398437

5

1.525

9E-05

0.41 52.48 52 0.40625 8.365

6E-05

0.42 53.76 53 0.414062

5

0.000

19985

0.43 55.04 55 0.429687

5

5.281

6E-07

0.44 56.32 56 0.4375 3.228

3E-05

67

0.45 57.6 57 0.445312

5

0.000

10851

0.46 58.88 58 0.453125 0.000

22337

0.47 60.16 60 0.46875 7.073

3E-06

0.48 61.44 61 0.476562

5

5.128

6E-05

0.49 62.72 62 0.484375 0.000

13178

0.5 64 64 0.5 1.972

2E-31

0.51 65.28 65 0.507812

5

1.839

7E-05

0.52 66.56 66 0.515625 7.078

6E-05

0.53 67.84 67 0.523437

5

0.000

15332

0.54 69.12 69 0.539062

5

3.014

1E-06

0.55 70.4 70 0.546875 3.228

3E-05

0.56 71.68 71 0.554687

5

8.999

6E-05

0.57 72.96 72 0.5625 0.000

17313

0.58 74.24 74 0.578125 1.045

1E-05

0.59 75.52 75 0.585937

5

4.741

1E-05

0.6 76.8 76 0.59375 0.000

10851

68

0.61 78.08 78 0.609375 1.049

8E-06

0.62 79.36 79 0.617187

5

2.057

8E-05

0.63 80.64 80 0.625 6.298

8E-05

0.64 81.92 81 0.632812

5

0.000

12612

0.65 83.2 83 0.648437

5

5.778

5E-06

0.66 84.48 84 0.65625 3.228

3E-05

0.67 85.76 85 0.664062

5

7.853

4E-05

0.68 87.04 87 0.679687

5

2.111

9E-07

0.69 88.32 88 0.6875 1.312

7E-05

0.7 89.6 89 0.695312

5

4.484

2E-05

0.71 90.88 90 0.703125 9.376

2E-05

0.72 92.16 92 0.71875 3.014

1E-06

0.73 93.44 93 0.726562

5

2.217

4E-05

0.74 94.72 94 0.734375 5.778

1E-05

0.75 96 96 0.75 3.506

E-31

0.76 97.28 97 0.757812

5

8.284

6E-06

69

0.77 98.56 98 0.765625 3.228

3E-05

0.78 99.84 99 0.773437

5

7.078

6E-05

0.79 101.12 101 0.789062

5

1.408

3E-06

0.8 102.4 102 0.796875 1.525

9E-05

0.81 103.68 103 0.804687

5

4.301

6E-05

0.82 104.96 104 0.8125 8.365

6E-05

0.83 106.24 106 0.828125 5.103

2E-06

0.84 107.52 107 0.835937

5

2.339

E-05

0.85 108.8 108 0.84375 5.406

6E-05

0.86 110.08 110 0.859375 5.281

6E-07

0.87 111.36 111 0.867187

5

1.045

1E-05

0.88 112.64 112 0.875 3.228

3E-05

0.89 113.92 113 0.882812

5

6.521

9E-05

0.9 115.2 115 0.898437

5

3.014

1E-06

0.91 116.48 116 0.90625 1.698

2E-05

0.92 117.76 117 0.914062

5

4.165

2E-05

70

0.93 119.04 119 0.929687

5

1.129

1E-07

0.94 120.32 120 0.9375 7.073

3E-06

0.95 121.6 121 0.945312

5

2.434

6E-05

0.96 122.88 122 0.953125 5.128

6E-05

0.97 124.16 124 0.96875 1.660

6E-06

0.98 125.44 125 0.976562

5

1.230

4E-05

0.99 126.72 126 0.984375 3.228

3E-05

1 128 128 1 4.437

3E-31

71

Appendix D

G =

6 s + 81

-------------------------------------------

8.16e-06 s^3 + 0.0001102 s^2 + 6.017 s + 81

Continuous-time transfer function.

r =

1.0e+02 *

-0.0002 + 8.5871i

-0.0002 - 8.5871i

-0.1346 + 0.0000i

n =

-13.5000

Kp =

2.0000e-04

Kp =

2.0000e-04

ans =

RiseTime: 115.6276

SettlingTime: 205.8826

72

SettlingMin: 0.9001

SettlingMax: 1.0000

Overshoot: 0

Undershoot: 0

Peak: 1.0000

PeakTime: 552.7287

% the original root locus of the PSCAD simulation

close all;

clear all;

clc;

num = [6, 81];

den = [8.16*10^(-6) 1.1016*10^(-4) 6.017 81];

G = tf(num, den)

figure;

rlocus(G)

r = roots(den)

n = roots(num)

Kp = .0002

Ki = 0.019;

num1 = [6, 81];

den1 = [8.16*10^(-6) 1.1016*10^(-4) 6.017 81+Kp 0];

G2 = tf(num1,den1);

figure;

rlocus(G2);

%step response with the PI controller

Kp = .0002

73

Ki = 0.019;

GC = tf([Kp, Ki], [1,0]);

GP = tf ([6 81],[8.16*10^(-6), 1.1016*10^(-4) 6.017 81]);

G1 = feedback(GC * GP , 1);

stepinfo(G1)

figure;

stepplot(G1);

Appendix E

Arduino code:

// include the library

#include <LiquidCrystal.h>

// all of our LCD pins

int lcdRSPin = 12;

int lcdEPin = 11;

int lcdD4Pin = 10;

int lcdD5Pin = 4;

int lcdD6Pin = 3;

int lcdD7Pin = 2;

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// initialize the library with the numbers of the interface pins

LiquidCrystal lcd(lcdRSPin, lcdEPin,

lcdD4Pin, lcdD5Pin, lcdD6Pin, lcdD7Pin);

#define PWM_PIN 5

#define PWM_MAX_COUNT 128

// the pin we use to control the relay

#define RELAY_PIN 7

#define MAX_VOLTAGE 4.1

#define MIN_VOLTAGE 0.0

// the time to leave the battery on in microseconds

#define BATTERY_TIME 50000000

long t0, t;

void setup()

{

Serial.begin(9600);

// set up the LCD's number of columns and rows:

lcd.begin(16, 2);

pinMode(A0, INPUT);

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pinMode(A1, INPUT);

pinMode(A3, INPUT);

pinMode(PWM_PIN, OUTPUT);

pinMode(RELAY_PIN, OUTPUT);

TCCR0A = _BV(COM0A0) | _BV(WGM00) | _BV(WGM01);

TCCR0B = _BV(WGM02) | _BV(CS01);

OCR0A = PWM_MAX_COUNT;

t0 = micros(); // record the starting time in microseconds

}

double Vreference = 100.0;

double Vref = Vreference / 46.0;

double kp = .3;

double ki = 0.8;

double T = 1.0/9600.0; // the peroid is 1/sampling frequency

double x = 0;

double x1 = 0; // recorded input x(k - 1)

double y = 0;

double y1 = 0; // recorded output y(k - 1)

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bool battery = true;

unsigned int k = 0; // keeps track of the sample.

int val;

int pwm_val;

double vin;

double current = 0.0;

void vref_lcd()

{

lcd.clear();

lcd.setCursor(0, 0);

lcd.print("Vref=");

lcd.print((int)(Vreference));

lcd.setCursor(0, 1);

lcd.print("Vt= 10");

lcd.print((int)(vin*46.0));

}

void vref_update()

{

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Vreference = (int)(analogRead(A3) * 15.0 / 1023.0) *10.0 +

50.0;

Vref = Vreference / 46.0;

}

void loop()

{

k++;

t = micros()-t0; // calculate elapsed time

if (battery == true)

{

digitalWrite(RELAY_PIN, HIGH);

if (t >= BATTERY_TIME)

{

battery = false;

digitalWrite(RELAY_PIN, LOW);

}

}

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if (k % 10 == 0)

{

vref_update();

}

val = analogRead(A0); // uncomment this line to read from A/D

converter

vin = (double)val / 204.6; //(double)val / 1023.0 * 5.0;

x1 = x;

x = (Vref - vin);

y1 = y;

y = y1 + kp*x + (ki*T - kp)*x1;

if (y < 0) y = 0;

if (y > MAX_VOLTAGE) y = MAX_VOLTAGE;

pwm_val = (int)(y * (double)PWM_MAX_COUNT / MAX_VOLTAGE);

analogWrite(PWM_PIN, pwm_val); // uncomment this to use the

difference equations

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if (k % 1000 == 0)

{

lcd.clear();

vref_lcd();

}

}

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Appendix F Budget given was $500 from the Electrical and Computer Engineering Department. Actual

spending was $687.59.