This document describes a project to improve power factor using static variable compensation. It contains 5 chapters that discuss: 1) an introduction to power factor and the objectives of the project, 2) a literature review and theoretical background, 3) the main components of the project including a zero crossing detector and triac, 4) the methodology including closed and open loop control approaches, and 5) results and conclusions from testing the project. The project aims to minimize the effects of reactive power flow on transmission lines by using a thyristor switched capacitor to generate reactive power and control the power factor, providing advantages over traditional capacitor banks and synchronous condensers.

1. An-Najah National University
Faculty of Engineering
Electrical Engineering Department
Power factor correction by Static Variable
Compensator
Prepared by:
Mohammed AbdallateefAbdaljawwad 11005554
Amjad Mohammad Adarba 11001713
Eyad Riad Amer 11001996
Supervised by:
Dr. Kamil Salih

2. Acknowledgement
we take thisopportunitytoexpress ourprofoundgratitude anddeepregardsto ourguide Dr.Kamil
Salihforhisexemplaryguidance,monitoring, continued support andconstant encouragement
throughoutthe course of thisproject.

3. Table of Contents
Chapter 1...................................................................................................1
Section 1.1 :Introduction..........................................................................1
Section 1. 2 . Objectives............................................................................2
Chapter 2...................................................................................................4
Section 2.1 : Literature review.................................................................4
Section 2.2 :Theoretical background..................................................... 5
Chapter 3: components of the project ……............................................8
Section 3.1 : zero crossing detector ………….…………………………8
Section 3.2 Triac ………….………………………………….…………9
Section 3.3 : Arduino ……………...…………………..…….…………10
Chapter 4 :Methodology…………………………………….……….….11
Section 4.1: Static Variable Compensation in closed loop control..….11
Section 4.2: : Static Variable Compensation in open loop control …..14
Section 4.2.1: PM meter ……………………………………………….15
Section 4.2.2: determine the firing angle …………………………….18
Section 4.2.3: Generating the firing angle………………….................24
Chapter 5: results and conclusions…………………………………...26
References ………………………………………………………..33
Appendix A……………………………………………………….34
Appendix B ……………………………………………………….37

4. List of Figures
 Figure.1: Load connectedto the Generatorthrough a Transmission
line..............................................................................................................5
 Figure.2: Lag betweenvoltage and current..........................................6
 Figure.3:Compensatedloadon The Transmission line.......................6
 Figure.4:Schematic of the relation betweenPF with the Apparent
power, Powerangle and Reactive power................................................6
 Figure 5: The current and voltage citation after correction................7
 Figure 6: circuit of zero crossing detection……………………………….8
 Figure 7: the Triac symbol and a simplifiedcross sectionofthe
device………………………………………………………………………………………9
 Figure 8: simulation of closedloopsystem ………………………….12
 Figure 9 : power factorbehavior at closedloopsystem ……………13
 Figure 10 : zero cross detectoroutput ……………………………….15
 Figure 11 : comparing betweenthe voltage signaland ZCD ……….16
 Figure 12 : triac operation……………………………………………19
 Figure 13:the shape of firing equation ……………………………..20
 Figure 14 : a graphicaldepiction of the bisection method…………21

5.  Figure 15:the code of bisectionmethod to determine firing angle..22
 Figure 16:changing alfa with changing load condition……………24
 Figure 17: arduino results 1 ……………………………………….26
 Figure 18:arduino results 2 ……………………………………….27
 Figure 19 :arduino results 3 ………………………………….…….28
 Figure 20 :arduino results 4 ………………………………….…….29
 Figure 21:arduino results 5 ………………………………….…….30
 Figure 22:comparing betweenalfa 1 and current ZCD …………...31
 Figure 23:comparing betweenalfa 2 and current ZCD …………...31
 Figure 24:comparing betweenalfa 3 and current ZCD …………...32
 Figure 25:comparing betweenalfa 4 and current ZCD …………...33

7. List of Tables
Table 1 : the relationbetweennumber of iterationand the max error
knowing that the value of alfa included in the interval of [0 , pi]…………23

8. :Nomenclatureor list of symbols
Z = Circuit impedance, Ω.
R = load Circuit resistance, Ω.
XL = load inductive reactance, Ω..
Xc= capacitor reactance
L= inductance value (Henry)
C= capacitive value (Farad)
I = Load current, A.
PF= power factor
Vrms= rms value of voltage at the shunt compensator
Vm= peak value of the voltage supplied by the source
P= real power consumed by the resistive part of the load
Qc= reactive power generated by the capacitor branch
Ql= reactive power consumed by the inductor (load branch)
S= apparent power transmitted from the source to the load
α= firing angle of the Triac
Ɵ= phase shift between voltage and currentat the end of the
transmission line
W= radial frequency of the source
f= frequency of the source in Hz
Ton= the time of the periodic signal that gives ONE value
ZCD= zero cross detector

9. ABSTRACT
The objective of this project is to improve power factor of transmission
lines using SVC (Static Variable Compensator). Static VAR Compensation under
FACTS uses TSC (ThyristorSwitched Capacitors) based on shunt compensation duly
controlled from a programmed microcontroller.
done bypower factor compensation wasPrior to the implementation of SVC,
.or switched capacitor bankssynchronous condenserlarge rotating machines such as
These were inefficient and because of large rotating parts they got damaged quickly.
This proposed system demonstrates power factor compensation using thyristor
switched capacitors.
Shunt capacitive compensation – This method is used to improve the
powerfactor. Whenever an inductive load is connected to the transmission line, power
factor lags because of lagging load current. To compensate for this, a shunt capacitor
is connected which draws current leading the source voltage. The net result is
improvement in power factor. The time lag between the zero voltage pulse and zero
current pulse duly generated by suitable operational amplifier circuits in comparator
mode are fed to two interrupt pins of the 8 bit microcontroller of Arduino family.
Thereafter program takes over to actuate appropriate number of opto-isolators duly
interfaced to back to back SCRs. This results in bringing shunt capacitors into the
load circuit to get the power factor till it reaches unity.
Further the project can be enhanced to thyristor controlled triggering for
precise PF correction instead of thyristor switching in steps.

10. 1
Chapter 1
Section1.1 : Introduction
Modern civilization depends mostly on electrical energy for agricultural, commercial,
domestic, industrial and social purposes [1]. The electrical energy is
exclusively generated, transmitted and distributed in the form of alternating
current(a.c.). Any load can be presented basically in three elements which are resistor
, inductor and capacitor. The resistor consumes active energy in which the electrical
energy takes a new form of energy (eg. Heat , mechanical, illumination …etc) while
the inductor and capacitor store the electrical energy in magnetic field and electric
field respectively which means the electrical energy still in its original form.
The actual amount of power being used, or dissipated, in a circuit is called real power.
Reactive loads, inductors and capacitors dissipate zero power, yet they drop
voltageand draw current giving the deceptive impression that they actually do
dissipate power. This “phantom power” is called reactive power[2]. More precisely
power dissipated by a load is referred to as real power where as power merely
absorbed and returned in load due to its reactive properties is referred to as reactive
power. However in nature, most of the loads are inductive loads consuming reactive
power and resulting in low lagging power factor, on the other hand capacitive load
(capacitor banks) generating reactive power and resulting in leading power factor. So
the capacitors and inductors loads have a opposite effect on power factor .
Effects of reactive power flow in line network
1- Poor transmission efficiency
Losses in all power system elements from the power station generator to the
utilization devices increase due to reactive power drawn by the loads, thereby
reducing transmission efficiency.
2- Poor voltage regulation
Due to the reactive power flow in the lines(higher current), the voltage drop in the
lines increases due to which low voltage exists at the bus near the load and makes
voltage regulation poor.
3- Low power factor
The operating power factor reduces due to reactive power flow in transmission lines.
4- Needof large sized conductor
Power factor correction allows to obtain advantages also for cable sizing. In fact, as
previously said, at the same output power, by increasing the power factor the current
diminishes. This reduction in current can be such as to allow the choice of conductors
with lower cross sectional area.
5- Increase in KVA rating of the systemequipment
Generators and transformers are sized according to the apparent power S. At the same
active power P, the smaller the reactive power Q to be delivered, the smaller the
apparent power. Thus, by improving the power factor of the installation, these
machines can be sized for a lower apparent power, but still deliver the same active
power.

11. 2
6- Reduction in the handling capacity of all systemelements
Reactive component of the current prevents the full utilization of the installed
capacity of all system elements and hence reduces their power transfer capability. A
power system is expected to operate under both normal and abnormal conditions and
under these conditions it is desired that the voltage must be controlled for system
reliability, the transmission loss should be reduced and power factor should be
improved (Rajesh Rajaramanet.al., 1998). In this paper the effect of line reactive
power flow on transmission efficiency, voltage regulation and power factor with and
without VAR compensation techniques are presented.
7- Penalties on consumers.
Consumers pay extra fees on bills for poor factor, e.g. in Palestine there is a penalty
for PF < 0.92
Section 1.2 : Objectives
The objective of the project is to minimize the effects of reactive power flow in the
line network, where the project will contributes the generator in supplying the load by
reactive power, so the project will reduce the power flow from generators to load,
therefore reducing the current, which in turn reduce the effects of reactive power flow
in the line network.
Now starting with the common methods which are used for solving poor PF of loads
problem, which are Capacitor Banks and Synchronous Condenser.[3]
Capacitor Banks is a method of adding capacitors in parallel at the load to generate a
part of the needed reactive power rather than the reactive power totally generated by
the power supply, they are a group of capacitors that are connected together
depending on how poor the PF load is, which reflects that the load requires more
reactive power. The main disadvantage of this method is that it requires high load to
sense the change on the power factor, therefore the generated reactive power by the
capacitor banks changes in steps and not in a smooth way, so we can't achieve a
specific PF at some loads.
Synchronous Condenser is a Synchronous motor which is over excited and most of
the time it's at no load or low load, itgenerates reactive power controlled accurately by
the field current, and the PF can be raised smoothly to achieve the required value.
Synchronous Condenser usually used for heavy load due its high cost. [3]
Taking into consideration the previous methods, the project tried to take the
advantages of both methods and avoid the disadvantages as much as possible. The
method of this project uses one large capacitor bank in series with a Triac. The firing
angle of the Triac controls the flow of reactive power from the capacitor. The
controller specifies the firing angle of the Triac to supply a part of reactive power of
the load depending on the reference PF. The main advantages of this method are low
cost with respect to the mentioned methods, this method is sensitive to any changes at
the load even for small changes and by this method a specific PF can be achieved.

12. 3
components blocks of the project

13. 4
Chapter 2
Literature review
Section 2.1: Citation relevant work and results
There are too many research on the ordinary methods of PF correction.
Arteche is a huge company in Spain which is a major manufacturer of
reactive compensation and harmonic mitigation products, this company
published a research aboutmany types of capacitor compensation, their
research shows differenttypes of compensation to different types of
load, and also shows the importanceof reactive power compensation.
A group of companies called ABB is a leader in power and automation
technologies that enable utility and industry customers to improve
performancewhile lowering environmental impact. ABB inserted the
TSC (thyristor switched capacitors ) as one of the mean technique in PF
correction methods and mentioned that this method could replace
synchronous condenser, where this method can correct the PF smoothly.
This method suffer from harmonics and ABB gave visualization for
solving this problem in their published paper (Technical Application
Papers No.8 Power factor correctionand harmonic filtering in
electrical plants).

14. 5
Section 2.2
Theoretical background
From the expertise that have been gained through past courses it was easier to deal
with the project. The PF correction has been mentioned in different courses such as
Electrical Circuits, Fundamental Machines and Power Systems. Many other courses
helped us in performing this project such as Power Electronic, 'Signals and Systems',
Drive of Electrical Machines and modeling using Matlab.
The following figuer.1 shows a load connected to a generator through a
transmission line, where Vs is the terminal voltage of the generator.
Figure.1
SL = 𝑃 + 𝑗𝑄𝑙
The power factor present the ratio between the real power consumed at the load to
the apparent power delivered to the load :
𝑃𝐹 =
𝑃
𝑆
=
𝑃
√𝑃2 + 𝑄𝑙2
Also the PF gives an indicator of the phase shift between current wave and voltage
wave, where PF is the cosine of the angle between current and voltage, a lagging PF
means that the current lags the voltage by an angle ( cos−1
𝑃𝐹) and a leading PF
means that the current leads the voltage by an angle ( cos−1
𝑃𝐹). As much as the
angle become bigger the power factor becomes smaller and vice versa.
In real life the loads always have lagging power factor due to inductive loads
Figure.2 shows a schematic for a current lags voltage with relatively low PF:

15. 6
Figure.2
For adding a shunt compensation (shunt capacitor branch ) to the load it will
contribute the generator in generating reactive power to the load .
Figure.3 shows the compensated load:
Figure.3
*note that the load will consume the same amount of real and reactive power
SL = 𝑃 + 𝑗𝑄𝑙
Shunt Compensation will generate reactive power to the load at a value of Qc that
will correct the PF by reducing the amount of reactive power delivered by the
generator which in turn reduce the apparent power :
𝑃𝐹 =
𝑃
𝑆
=
𝑃
√𝑃2 + ( 𝑄𝑙 − 𝑄𝑐)2
Figure.4: schematic the relation between PF with apparent power , power angle and
reactive power Where
Figure.4

16. 7
Figure.5 shows the current and voltage citation after correction:
Figure.5
We notice that the enhanced PF the smaller phase shift be.
Now the importance of PF correction is that the reactive power transmitted will be
smaller so the apparent power will be reduced
𝑆. 𝑜𝑙𝑑 = √ 𝑃2 + 𝑄𝑙2
𝑆. 𝑛𝑒𝑤 = √ 𝑃2 + ( 𝑄𝑙 − 𝑄𝑐)2
Which in turn reduce the current at the transmission line
𝐼. 𝑜𝑙𝑑 =
𝑆. 𝑜𝑙𝑑
𝑉
=
√𝑃2 + 𝑄𝑙2
𝑉
𝐼. 𝑛𝑒𝑤 =
𝑆. 𝑛𝑒𝑤
𝑉
=
√𝑃2 − ( 𝑄𝑙 − 𝑄𝑐)2
𝑉
Then the voltage drop will decrease , the losses at the transmission line will reduce ,
which enhance the efficiency of the transmission line ,avoid extra fees on bills and the
rated power of the system equipment will be reduced ,that’s means we need smaller
sized and cheaper equipment and transmission lines.

17. 8
Chapter 3: main components of the project
Section 3.1: zero crossing detector
The zero cross detection circuit is the most critical part for designing a PF
meter in our project. This circuit will watch the input voltage and current waveforms
and detect when this waveforms cross the zero axis .
Zero cross detection circuits are mainly used in cases when the PF needs to be
measured by micro controller. In that case, the micro-controller needs to know the
zero cross detection point of the voltage waveform, so that it can calculate the angle
offset to send the trigger pulse to the gate of the triac.
Here is an example calculation. Suppose that the AC power oscillates in a
50Hz cycle. This means that each cycle will take 1/50Hz = 20 mSec to be completed.
During those 20mSec, the waveform will cross the zero point two times, one at the
beginning and one in the middle of the cycle, that will be after 20/2 = 10mSec.
If we want the capacitor to inject reactive power from applying a half
waveform of the voltage , then the microcontroller needs to send a pulse in the middle
of each semi-cycle. Thus, a pulse must be sent after 5mSec after each time the
waveform passes the zero point. For this to be done, the microcontroller will watch
the zero cross detection circuit (ZCD) for a pulse. When the ZCD send this pulse,
the micro controller will count 5 mSec and then will trigger the gate of the triac.
The following circuit will perform a Zero Cross Detection circuit. This circuit
is very stable and accurate, and has a controllable pulse width. Another great
advantage is that because of the transformer, this circuit has a complete galvanic
isolation with the mains supply so that it makes it completely safe and risk free of
destroying the microcontroller due to power peaks.[4]
Figure 6

18. 9
Section 3.2 : Triac
The Triac or bi-directional Thyristor, is a device that can be used to pass or block
current in either direction. It is therefore classed as an AC power control device. It is
equivalent to two Thyristor in anti-parallel with a common gate electrode. As only
one device is required there are cost and space savings.
Figure 7.
The Triac has two main terminals. TE1/ TE2 (power in and load out) and a single gate
connection. The main terminals are connected to both p and n regions since the
current can be conducted in either direction. The gate is similarly connected, since a
Triac can be triggered by both negative and positive pulses.
The ON state voltage or current characteristics resembles a Thyristor. The Triac static
characteristics show that the device acts as a bi-directional switch. The condition
where terminal TE2 is positive with respect to terminal 1 is denoted by the term
TE2+. If the Triac is not triggered the low level of leakage current increases as the
voltage increases until the break over voltage V is reached and then the Triac turns
ON. The Triac can be triggered below V by a pulse to the gate, provided that the
current through the device exceeds the latching current I before the trigger pulse is
removed. The Triac has a holding current value below which conductance cannot be
maintained.
If terminal 2 is negative with respect to terminal TE2 the blocking and conducting
conditions are similar to the TE2+ condition, but the polarity is reversed. The Triac
can be triggered in either direction by both negative or positive pulses on the gate.
The actual values of gate trigger current and holding current as well as latching
current can be slightly different in the different operating quadrants of the Triac due to
the internal structure of the device. [5]

19. 10
Section3.3: Arduino
The Arduino Uno isa microcontroller board based on the Atmega328
which can be programmed withthe Arduino software. Ithas 14
digital input/outputpins(of which 6 can be used as PWM outputs), 6
analog inputs, a 16 MHz ceramic resonator, the Arduino Uno can be
powered viathe USB connection or with an external power supply.
The power sourceis selected automatically.
The Atmega328 has32 KB memory (with 0.5 KB used for the boot
loader). It also has 2 KB of SRAM and 1 KB of EEPROM (which can be
read and written with the EEPROM library).
"Uno" means onein Italian and is named to mark the upcoming
release of Arduino 1.0. TheUno and version 1.0 will be the reference
versionsof Arduino, movingforward. TheUno is the latest in a series
of USB Arduino boards, and thereference modelfor the Arduino
platform; for a comparison with previousversions. [6]

20. 11
Chapter 4: Methodology
This chapter will explain the used method for calculating the power factor, firing
angle for the triac and time of phase shift also dealing with zero cross detector and
Arduino programming.
In the last semester it was discussed that the Static Variable Compensation mainly
works on measuring the PF of the load then the controller will keep adjusting the
amount of reactive power that should be injected to the load by controlling the firing
angle of the traic until the new PF will be equal to reference (needed) PF which means
that the methodology used a closed loop system.
In this semester, due to the high difficulty finding some of important tools to achieve
the project in mentioned methodology (closed loop method), it could be found some
of these tools but with a high cost. So we concentrated on the main units of the project
which are PF meter and control unit which responsible to generate the firing angle to
the triac, so the applied voltage to the capacitor bank is controlled then the amount of
reactive power generated from the capacitor and injected to the load also is controlled.
This chapter will include two sections.
At first section we will discuss the closed loop methodology in correcting the power
factor which is very efficient and practical method .
The second section discuss use open loop method which means there is no feedback
comes from the load to the controller, because actually to deal with a real load we
need instruments tools such as current and potential transformers to convert the real
voltages and currents to measurable values suites the control unit, but unfortunately
these instruments transformers are difficult to find at the market

21. 12
Section4.1:Static Variable Compensationin closedloopcontrol
In the last semester we built simulation on MATlap for static variable compensation
in closed loop control manner, see figure
Figure 8
As seen from the figure the module consist of load, measuring instrument for the
load's current and voltage, PF meter, a capacitor bank connected in series with a triac,
and most critical part which is the control unit.
The control unit will keep adjusting the value of firing angle until that the the
measured PF on the load exactly equal the reference PF, where as seen the control
unit take the measured PF as feedback. The main element in the control unit is the
integration which actually the controller, this controller obviously works in integral
manner, where the output of this element is additives depending on the
inputs(reference PF and the feedback measured PF), it can be noted that when the

22. 13
reference PF equals the measured PF then the difference between them is zero,
therefore the output of the integration unit is constant or DC value, this DC value is
translated to the value of firing angle (alfa) for the triac by using a saw tooth oscillator
and comparators. The module is able to correct the PF under changing load and
achieve the reference PF, the following figure shows how was the module able to
correct the PF under changing load and achieving the reference PF(0.9 in our case).
Figure 9
The main advantages of this method are
 The simplicity of its control specially using Arduino
 In this method there is need only for a PF meter at the load
 There is no need for KW meter at the load and there is no need to measure the
voltage and the current at the load because the controller specify the value of
the firing angle depending on the value of the PF on the load and the reference
PF
 Ability to supply exact amounts of reactive power to achieve specific
reference PF regardless for light or heavy load, where traditional ways to
correct the PF face problems to deal with different load sizes
 The module is able to deal with the changing the voltage at the bus of the load

23. 14
Section 4.2: Static Variable Compensation in open loop control
In this semester we obliged to work in open loop Static Variable Compensation
control system because to deal with a real load we need instruments tools such as
current and potential transformers to convert the real voltages and currents to
measurable values suites the control unit (control’s voltage-level is low), but
unfortunately these instruments transformers are difficult to find at the market, and
because we couldn’t bring instruments transformers we didn’t try to test our project
on a real load bring such as an induction motor.
Open loop method which means there is no feedback comes from the load to the
controller, so the accuracy to achieve the reference PF will be less than it for closed
loop
In our methodology of open loop Static Variable Compensation we need a PF meter
and KW meter, we were able to build a PF meter as will be discussed in this section
but we assumed that we have constant consumption of real power instead of KW
meter and also a constant voltage at the load, this section will show why these
assumptions made. So briefly in our project we will show how the controller changes
the value of the firing angle depending on the measured PF.
The used methodology consists of mainly two parts. First part is building a PF meter.
Secondly, determining the suitable value of the firing angle, which is supposed to
control suitable voltage to control the amount of reactive power the must be generated
to the load achieve the reference PF.

24. 15
Section4.2.1 : PF meter
The firstpart of calculatingthe PFisto findthe phase shiftbetweenthe voltage andcurrent
waveforms,thatmeanswe have tofindthe time difference betweenwhenthe voltage cross
the zero axisandwhenthe currentwave cross the zeroaxis,inorder to applythe previous,a
ZeroCross DetectorCircuit(ZCD) isused.
As mentionedbeforeZCDcircuitgivespulse phase modulationPPMtogive an indication
whenthe signal (sinusoidalinthe project) startto rise or fall fromthe zeroaxis,whichgive
a duplicate the frequencyatthe output,wheneverthatoccursthe generatedpulse givesan
indicationthatthere isa zerocross inthisplace .
The followingfigure showsthe outputsignal fromZCDcircuit
Figure 10
However,if bothvoltage andcurrentappliedtoZCDcircuits,we can findthe phase shift
betweenZCDof voltage andZCD of current andthat meanswe findthe phase shiftbetween
the voltage andthe current waveformsthemselves.
the current shouldpassthrougha resistance inordertoconvertit to a voltage:Note
waveformbecause the ZCDcircuits dealswithvoltage input,andthe resistance makesno
phase shiftforthe current.
The followingfigure showsthe relationbetweenvoltageorcurrentwaveformwithitsZCD

25. 16
Figure 11
The secondpart is to use the PPMfromthe twoZCD circuitsto determine the powerfactor,
the ZCD for the voltage andthe current will be connectedtoarduinoinput,pinforeach(D2
for voltage andD3 for current),we wrote a code to findoutthe time betweenthe ZCD
pulsesof the voltage andthe ZCD pulsesof the current thencalculate the phase shift
betweenthesetwoinputs,whichmeansthatwe foundthe phase shiftbetweenthe original
waveformsof voltage andcurrent.
There isa functionatthe arduinocalled“micros()”,whichisabuiltintimerstartto count in
microsecondsince the processerstartsto work,we use thisfunctiontocapture the time
storedinthe micros functionwhenthe voltage crossesthe zero,afterthatwe capture the
time storedinthe microsfunctionwhenthe currentcrossesthe zero,sosimplythe time of
phase shiftwill be the difference betweenthe capturedtime of current ZCDand the
capturedtime of voltage.
Here is an example of simple microsfunctioncode todeterminethe knowntime,where in
thiscode we capture the time of the micros andsimplyapplyadelayby1000 mille second
and againcapturedthe storedtime at microsthenwe findthe differencebetweenthe two
captures,the difference will me inmicrosandto findthe resultinmille secondwe dividethe
resultby1000, finallywe showedthe resultatthe monitortocompare betweenthe code
resultandthe appliedtime delay:

26. 17
The followingshowsthe monitoroutputresults which shows that the difference in reading
the micros function match the supposed delay (1000 Milles).
There isa small errorineach cycle of the programequal to 20 microsecondat most which is
high precision.
Aftercalculatingthe time betweenthese twoinputs,the phase shiftcanbe calculatedin
linearmannerwhere full periodoccursafter20 mille seconds(1/freq=1/50second)
correspond360 degree,sothe relationbetweenphaseshiftandtime of phase shiftis:
𝑝ℎ𝑎𝑠𝑒 𝑠ℎ𝑖𝑓𝑡 = 𝑡𝑖𝑚𝑒 𝑠ℎ𝑖𝑓𝑡 ∗
360
20
Then the PF will be equal to cosin the phase shift in radial as in the equations:
Ɵ = 𝑝𝑎𝑠ℎ𝑒 𝑠ℎ𝑖𝑓𝑡 ∗
𝜋
360
𝑃𝐹 = 𝑐𝑜𝑠Ɵ

27. 18
Section4.2.2:determine the firing angle
In order to control the generated reactive power from the capacitor bank we have to
control the value of either the capacitance or the applied voltage to the capacitor bank
according to the following equation:
𝑄𝑐 = 𝑉𝑟𝑚𝑠2
∗ 𝑊 ∗ 𝐶
Traditional method control the capacitance to control the reactive power generated, in
our project we control the applied voltage to the capacitor bank.
The main relation is between the firing angle (α) of the triac and the applied voltage
according to the following equations:
𝑉𝑟𝑚𝑠 = √
1
𝜋
∫ (𝑉𝑚 sin 𝑊𝑡)2
𝜋
𝛼
𝑑𝑤𝑡
= √
𝑉𝑚2
𝜋
∫ (sin 𝑊𝑡)2
𝜋
𝛼
𝑑𝑤𝑡
= √
𝑉𝑚2
𝜋
∫
1
2
(1 − 𝑐𝑜𝑠2𝑤𝑡)
𝜋
𝛼
𝑑𝑤𝑡
= √
𝑉𝑚2
2𝜋
[𝑤𝑡 −
𝑠𝑖𝑛2𝑤𝑡
2
] ; 𝑤𝑡 =∝ 𝑡𝑜 𝜋
= √
𝑉𝑚2
2𝜋
[𝜋 −
𝑠𝑖𝑛2𝜋
2
− 𝛼 +
𝑠𝑖𝑛2𝛼
2
]
= √
𝑉𝑚2
2𝜋
[𝜋 − 𝛼 +
𝑠𝑖𝑛2𝛼
2
]
= √
𝑉𝑚2
2𝜋
[𝜋 − 𝛼 +
𝑠𝑖𝑛2𝛼
2
]
Then 𝑉𝑟𝑚𝑠 = 𝑉𝑚√
1
2𝜋
[𝜋 − 𝛼 +
𝑠𝑖𝑛2𝛼
2
]

28. 19
The following figure shows the relation between the firing angle of the triac and the
applied voltage to the capacitor
Figure 12
As mentioned before we assumed that the consumption of real power of the load is
constant because it is hard to build KW meter also we assumed that the voltage at the
load is constant and equal to the nominal voltage, we also assumed that the worst PF
at the load is 0.4.
Now after finding the PF we found the required amount of generated reactive power
according to the following equation
𝑄𝑐 = 𝑃 (tan (acos𝑃𝐹𝑜𝑙𝑑) − tan(acos 𝑃𝐹𝑛𝑒𝑤))
Now to generate required reactive power to achieve reference PF the voltage should
be set according to the following
𝑄𝑐 = 𝑉𝑟𝑚𝑠2
∗ 𝑊 ∗ 𝐶
Then
𝑉𝑟𝑚𝑠 = √
𝑄𝑐
𝑊 ∗ 𝐶

29. 20
To control the applied voltage, the firing angle (α) should be set according to
following equations
𝑉𝑟𝑚𝑠 = 𝑉𝑚√
1
2𝜋
[𝜋 − 𝛼 +
𝑠𝑖𝑛2𝛼
2
]
With some manipulations with this equation we reached the following equation
sin2α − 2α = 𝑐𝑜
Where 𝑐𝑜 =
𝑉𝑟𝑚𝑠2
𝑉𝑚2
∗ 4𝜋 − 2𝜋
To solve this equation we use numerical method called Bisection Method
The shape of sin 2α − 2α will be as followed
Figure 13
When alfa included inside the interval of [0,π],
it can be concluded that the value of “co” has a range between 0 and -6.3

30. 21
-Bisection method
The bisectionMethod,whichisalternativelycalledbinarychopping,interval halving,or
Bolazan’s method,isone type of incrementalsearchnumerical methodinwhichthe interval
isalwaysdividedinhalf.If afunctionchangessignoveraninterval,the functionvalueatthe
midpointisevaluated.The locationof the rootsisthendeterminedaslying atthe midpoint
if the subinterval withinwhichthe signchange occurs.The processisrepeatedtoobtain
refinedestimates.A simple algorithmforthe bisectioncalculatedinthe nextstepsanda
graphical depictionof the methodisprovidedin the followingfigure [7].
Figure 14

31. 22
The main methodologyof programmingthe bisectionmethod(numerical)
Step1-Choose lowerxl andupperxu guessesforthe rootsuch that the functionchanges
signoverthe interval.Thiscanbe checkedbyensuringthatf(xl)*f(xu)<0
Step2-Anestimate of the root xris determinedby
xr=(xl+xu)/2
Step3-Make the followingevaluationstodetermine inwhichsubinterval.Thereforeset
xu=xrand
a) if f(xl)*f(xr)<0,the rootliesinthe lowersubinterval.Therefore,setxu=xrandreturnto
step2
b) if f(xl)*f(xr)>0,the rootliesinthe uppersubinterval.Therefore,setxl=xrandreturnto
step2
c) if f(xl)*f(xr)=0,the root equal x;terminate the computation.
Dependsonthe previous,the followingfigure showsthe bisectionusedcode toestimate the
value of alfain orderto control the rms voltage appliedtothe capacitorto control the
injectedreactive powertothe loadto correctthe powerfactorof the load.
Figure 15

32. 23
as the numberof iterationincrease the errorwill rapidlydecrease:Note
followingtable showsthe relationbetweennumberof iterationandthe max errorknowing
that the value of alfaincludedinthe interval of [0, pi].
Number of iterations Max Error (%) Max Error (degree)
1 50
90
2 25
45
3 12.5
22.5
4 6.25
11.25
5 3.125
5.625
6 1.56
2.808
7 0.78
1.404
8 0.39
0.702
9 0.19
0.342
10 0.097
0.1746
Table 1

33. 24
Section4.2.3:Generating the firing angle
Thissectioninterestedatthe usedmethodologiestogenerate the firingangle tothe triacin
orderto control the appliedvoltageatthe capacitorbank.
Simplythe projectuse twodifferentmethodologiestogenerate alfa afterfindingitin
numerical methodas mentionedinthe previoussectionof thischapter.
-first methodology :-
The firstmethodologymakesatestat everypossible”time point”of the period tofindoutif
thisisthe correct time togenerate alfaor not
The test mainly comparesbetweenthe foundedalfaintime domainwiththe difference
betweenthe presenttime andthe time where the ZCDof the voltage start, if theyare equal
thena highvoltage will appliedtooutputpinfora small periodof time (0.5in our project),
thenthe program start fromthe beginningtorepeatthisgenerationateverycycle with
difference firingangle dependsonthe new conditionof the load.
So if there isa newloadpowerfactor, the controllerwill make averyfast new firingangle to
control the amountof injectedreactive power.
Figure 16

34. 25
- secondmethodology :-
The secondmethodology hasthe same testwhichcompare betweenthe foundedalfa in
time domainwiththe difference betweenthe presenttime andthe time wherethe ZCDof
the voltage start,alsoif theyare equal thena highvoltage will appliedtooutputpinfora
small periodof time (0.5in our project),themaindifference isthat the programgenerates
the same alfa for50 times(one second) bycalculatingitonce inthe second,thenthe
program start fromthe beginningtorepeatthisgenerationateverysecondwithdifference
firingangle dependsonthe newconditionof the load.
Thismethodologyalsohasafast and practical response tothe changinginthe load
conditions,
Althoughthe second methodologyhas slowerresponse,it hasgoodaccuracy and evermore
practical effectiveness.

35. 26
Chapter 4: results and conclusions
This chapter shows the ability of the project to correct the PF of the load by
generation the firing angle to control the applied voltage of the capacitor bank, the
results shows both of the positive and negative parts of the sinusoidal signal have a
generated alfa related to the measured PF of the load,
As mentioned before. the PF calculated related to the time of phase shift between the
voltage and current ZCD which frequency duplicated from the sinusoidal signal, this
because of the ZCD should applied to both positive and negative part of the sin wave,
Using arduino monitor, we get the result of calculating the time of phase shift, PF and
firing angle.
The fpllowing figures shows that results for different values :-
Figure 17

36. 27
Figure 18

37. 28
Figure 19

38. 29
Figure 20

39. 30
Figure 21

40. 31
Also we get results from the oscilloscope to get the results comparing different values
of the generated firing angle with respect ZCD of the voltage as shown in the
following figures :-
Figure 22
Figure 23

41. 32
Figure 24
Figure 25

42. 33
References:
[1] B.R.Gupta, (1998), Power System Analysis And Design, Third Edition ,
S.Chandand Company Ltd
[2] Van Cutsem T., 1991, “A method to compute reactive power margins with respect
to voltage collapse”, IEEE Transactions on Power Systems, pp 145
[3] Stephen J. Chapman,2004, Electric Machinery Fundamentals, p(363,364).
[4] http://pcbheaven.com/wikipages/Dimmer_Theory
[5]http://www.sprags.com/summary.html
http://arduino.cc/en/Main/arduinoBoardUno[6]
[7] book-numerical method for engineering, 6th
Edition 2009 Chapra Canal, page 124

43. 34
Appendix A
int VZD = 2; // voltage zero cross at pin 2
int IZD = 3; // current zero cross at pin 3
int fire =8;// output pin for fireing angle pin 8
float tv; // initial time of shifting calculatio from voltage crossing
float ti; // fianl time of shifting calculatio from current crossing
float Ton;
double theta;
const float pi = 3.14;
double PF;
float alfa;
float alfa1;
float TF=4000;
int flag1=0;
int flag2=0;
int flag3=0;
int flag4=0;
double co;
double Vrms;
int Vm=326;
int P = 5000;
int C=0.0014;
double PFn=0.95;
double xl;
double xu;
double xr;
double xrold;
int iter;
double fxl;
double fxr;
double test;
double ea;
int es=2;
double Qc;
double ea1;
void setup() {
Serial.begin(9600);
pinMode(VZD,INPUT);
pinMode(IZD,INPUT);
pinMode (fire,OUTPUT);
}
void loop() {
// finding the time of voltage ZCD
while (digitalRead(VZD) != 0 ){
tv = micros() ;
flag3=1; // allow to genrate alfa
flag4=1; // allow the current code
}

44. 35
if ((micros()-tv)>=TF && flag3==1){ // generat alfa if it's in the regon between ZCD of voltage
and current
digitalWrite (fire , HIGH );
delay (0.5);
digitalWrite (fire , LOW );
flag3=0;
}
//finding the time of current ZCD
if (flag4==1){
while (digitalRead(IZD) != 0 ){
ti = micros() ;
flag1=1;
}
}
if (flag1==1){ // there is a measured time shift between the two inputs
flag1=0;
Ton = ti-tv; // find the time between tv and ti
Ton=Ton/1000; // transfer the time phase shift to milli second
if (Ton >0.1 && Ton <4.359){ // the accepted values of Ton related to the accepted values of PF
// calculating PF
theta = Ton * pi/10 ; // finding the phase shift angle in rad
PF=cos(theta ); // calculating the power factor
// finding the firing angle using bisectional method
xr=0;
xl=0;
xu=pi;
Qc=P*(0.328- tan(theta));
Qc=abs (Qc);
Vrms = sqrt(Qc/C*100*pi);
co=((Vrms*Vrms)/8419)-(6.28); // co=((Vrms*Vrms)*4*pi/(Vm*Vm))-(2*pi)
iter = 0;
while (iter <=10 && ea<es ){
xrold=xr;
xr=(xl+xu)/2;
iter++;
if (xr != 0){
ea1=(xr-xrold)/xr;
ea =(abs(ea1))*100;
}
fxl=sin (2*xl)-(2*xl)-co;
fxr=sin (2*xr)-(2*xr)-co;
test = fxl*fxr;
if (test<0){
xu=xr;
}

45. 36
else if (test >0){
xl=xr;
}
else {
ea=0;
}
}
alfa = xr;// firing angle in rad
TF=alfa*10000/pi;// finding the fiering angle as time in micro second
flag2=1; // there is allowed values to print
}
else if (Ton <=0.1 && Ton >=0){
theta = Ton * pi/10 ;
PF=cos(theta );
alfa=pi;
flag2=1;//there is allowed values to print
}
else if (Ton <=5 && Ton >=4.359){
theta = Ton * pi/10 ;
PF=cos(theta );
alfa=0.01;
flag2=1;//there is allowed values to print
}
alfa1= alfa*180/pi; // firing angle in degree...only for monitoring
TF=alfa*10000/pi;// finding the fiering angle as time in micro second
if (flag2==1){ // variables to be prented
flag2=0;
Serial.println("time of phase shift : ");
Serial.println(Ton);
Serial.println("");
Serial.println("value of power factor");
Serial.println(PF);
Serial.println("");
Serial.println("value of fiering angle");
Serial.println(alfa1);
Serial.println("");
}
}
if ((micros()-tv)>=TF && flag3==1){ // generat alfa if it's not in the regon between ZCD of
voltage and current
digitalWrite (fire , HIGH );
delay (0.5);
digitalWrite (fire , LOW );
flag3=0;
}
}

46. 37
Appendix B
int VZD = 2; // voltage zero cross at pin 2
int IZD = 3; // current zero cross at pin 3
int fire =8;// output pin for fireing angle pin 8
float tv; // initial time of shifting calculatio from voltage crossing
float ti; // fianl time of shifting calculatio from current crossing
int flag1=0;
float Ton;
double theta;
const float pi = 3.14;
int flag2=0;
double PF;
double alfa;
float TF=4;
int flag3=0;
int counter;
double co;
double Vrms;
int Vm=326;
int P = 5000;
int C=0.0015;
double PFn=0.92;
double xl;
double xu;
double xr;
double xrold;
int iter;
double fxl;
double fxr;
double test;
double ea;
int es=2;
double Qc;
double ea1;
int counter ;
void setup() {
Serial.begin(9600);
pinMode(VZD,INPUT);
pinMode(IZD,INPUT);
pinMode (fire,OUTPUT);
}
void loop() {
while (digitalRead(VZD) != 0 ){
tv = micros() ;
flag3=1; // can search for TF
}

47. 38
}
while (digitalRead(IZD) != 0 && flag3==1 ){
ti = micros() ;
flag1 =1;
flag3=0;
}
if (flag1==1){ //PF meter
flag1 =0;
Ton = ti-tv; // find the time between tv and ti
Ton=Ton/1000; // transfer the time phase shift to milli second
flag2=1;
if (Ton > 5){
flag2=0;
}
if(PF>0.95|| PF<0.2){
flag1=0;
}
}
if (flag1 ==1){//dteremining the value of alfa (firing angle) using neumerical Bisectional metheod
theta = Ton * pi/10 ; // finding the phase shift angle in rad
PF=cos(theta ); // calculating the power factor
PF=abs (PF);
Serial.println("time of phase shift : ");
Serial.println(Ton);
Serial.println("");
Serial.println("value of power factor");
Serial.println(PF);
Serial.println("");
flag2=0;
xr=0;
xl=0;
xu=pi;
Qc=P*(0.328- tan(theta));
Vrms = sqrt(Qc/C*100*pi);
co=((Vrms*Vrms)*12.56/(106276))-(6.28); // co=((Vrms*Vrms)*4*pi/(Vm*Vm))-(2*pi)
iter = 0;
while (iter <=10 || ea<es ){
xrold=xr;
xr=(xl+xu)/2;
iter++;
if (xr != 0){
ea1=(xr-xrold)/xr;
ea =(abs(ea1))*100;
}
fxl=sin (2*xl)-(2*xl)-co;
fxr=sin (2*xr)-(2*xr)-co;
test = fxl*fxr;
if (test<0){
xu=xr;
}
else if (test >0){

48. 39
xl=xr;
}
else {
ea=0;
}
}
alfa = xr;
if(PF>0.92){
alfa=pi;
}
alfa=alfa*180/pi;
TF=alfa*20/360;// finding the fiering angle as time in mille second
Serial.println("value of fiering angle");
Serial.println(alfa);
Serial.println("");
}
counter = 0;
while (counter<100){
while(digitalRead(VZD) != 0){
TF = TF+1;
delay (TF);
digitalWrite (fire, HIGH);
delay (1.1);
digitalWrite (fire, LOW);
counter ++;
}
}
}