pv powered dc motors design and analysis

7/25/2019 Pv Powered Dc Motors Design and Analysis

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Hashemite University

Department of Electrical engineering

2015-2016

Terminal Characteristics of DC Shunt

Motor Powered by Photovoltaic

Generator via DC- DC Converter

Supervised y!

Dr"#ohammad $idyan

Done y!

#ohammed %a$ashdeh &reen Shiyahin

&'d &lrahman (aarteh )haith %yyashi

&'d &lrahman Da$ood

Abstract


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*his document presents the dynamical analysis of D+ shunt motor

po$ered 'y ,hotovoltaic ,./ generator via D+- D+ 'uc-'oost

s$itch mode converter at dierent solar irradiance levels" &t the full

solar intensity the ma3imum po$er point of current4voltage 4.

characteristic of the ,. modules is designed to 'e at the rated

conditions of the motor" *he nonlinear pro'lem of 4. characteristics

of the ,. modules and that of the magnetiation curve of the

ferromagnetic materials of the motor it is appro3imated 'y

polynomial curve 7tting" & 'uc - 'oost converter provide an output

voltage constant/ $hich may 'e less than or greater than the input

voltage varia'le/" *he output voltage polarity is opposite to that of

the input voltage to the motor"

Keywords: ,hotovoltaic +ells Steady-State 8utput +haracteristics

#agnetiation curve of dc shunt motor +ontinuous mode of 'uc 'oost

converter "

2


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Table of contents

Chapter 1.

ntroduction"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

"""6

Chapter 2. ,. )enerator #odel and #ain

+haracteristics"""""""""""""""""""""""""""""""""""""""""""""10

Chapter 3. D+-D+

+onverters99999"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""1:

Chapter 4. D+

#achines9""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""2;

Chapter 5. System

E


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Table of Figures

Figure !E


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Figure ( !*he circuit con7guration of oost

converter999999999""""""""""20

Figure ) !+ircuit diagram of a 'ucC'oost converter9999"""99"

999""9""20

Figure * ! *he t$o operating states of a 'ucC'oost

converter99"""9"9"99"""21

Figure !aveforms of current and voltage in a 'ucC'oost

converter operating

in continuous mode99999""""

999999999999""9921

Figure "!E


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Figure "*!the tor


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Cha+ter !

,ntroduction

?


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Chapter 1: ,ntroduction

Almost every mechanical movement that we see around us is accomplished by amotor. Electric machines are a means of converting energy. Motors take electrical

energy and produce mechanical energy. Electric motors are used to power hundreds of

devices we use in everyday life. Motors come in various sizes. Huge motors that can

take loads of !!!"s of Horsepower are typically used in the industry. #ome e$amples

of large motor applications include elevators% electric trains% hoists% and heavy metal

rolling mills. E$amples of small motor applications include motors used in

automobiles% robots% hand power tools and food blenders. Micro&machines are

electric machines with parts the size of red blood cells% and find many applications in

medicine. '(

A )* machines are usually classified on the basis of their field e$citation method. +n

shunt ).* motor connects the armature and field windings in parallel or shunt with a

common ).*. power source. )* series machines have the field circuit in series with

the armature where both field and armature currents are identical. ,ermanent&magnet

machines% on the other hand% have only one circuit -armature winding and the flu$generated by the magnets is constant. *ompared with conventional electrical

machines% permanent&magnet machines e$hibit higher efficiency% higher power to

weight ratio and simpler construction. '/( 0he shunt motor has good speed regulation

even as the load varies% but does not have the starting tor1ue of a series ).* motor. +t

is typically used for industrial% ad2ustable speed applications% such as machine tools%

winding3unwinding machines and tensioners.'4(

:


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,hotovoltaic"s offer consumers the ability to generate electricity in a clean% 1uiet and

reliable way. ,hotovoltaic systems are comprised of photovoltaic cells% devices that

convert light energy directly into electricity. 5ecause the source of light is usually the

sun% they are often called solar cells. 0he word photovoltaic comes from 6photo%7

meaning light% and 6voltaic%7 which refers to producing electricity. 0herefore% the

photovoltaic process is 6producing electricity directly from sunlight7% ,hotovoltaics

are often referred to as ,8.

,8 systems are being installed by 0e$ans who already have grid&sup& plied electricity

but want to begin to live more independently or who are concerned about the

environment.

9or some applications where small amounts of electricity are re1uired% like emergency

call bo$es% ,8 systems are often cost 2ustified even when grid electricity is not veryfar away. hen applications re1uire larger amounts of electricity and are located

away from e$isting power lines% photovoltaic system scan in many cases offer the

least e$pensive% most viable option.

+n use today on street lights% gate openers and other low power tasks% photovoltaic"s

are gaining popularity in 0e$as and around the world as their price declines and

efficiency increases. ';(

A )*&)* converter is a vital part of alternative and renewable energy conversion%

portable devices% and many industrial processes. +t is essentially used to achieve a

regulated )* voltage from an unregulated )* source which may be the output of a

rectifier or a battery or a solar cell etc. #9E0 -switch gate signal accordingly. +t is

basically governed by a switching logic% thus constituting a set of subsystems

depending upon the status -on& off of the switch. +n the well&known pulse width

modulation -,M techni1ue% the control is accomplished by varying the duty ratio

B


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of an e$ternal fi$ed fre1uency clock through one or more feedback loops% whenever

any parameter varies. '?(

+n this document% the main contributions are the dynamical analysis of )* shunt

motor fed by photovoltaic cells at different solar intensities as compared with the case

of supplying the motor by fi$ed terminal voltage via buck&boost converter.

Additionally% the ma$imum power point of the photovoltaic cells is designed to be at

the rated conditions of the machines when the ,8 array is fully illuminated. 0he

nonlinearity of the magnetization curve of the ferromagnetic materials of the machine

in shunt motor and that of the +38 characteristics of the photovoltaic cells have been

included by polynomial curve fitting .

0he document presents 0he nonlinear dynamical model of the )* shunt motor .Also

outlines the design and main characteristics of the photovoltaic cells with main

characteristics of the buck&boost converter. 9inally% 0he numerical simulation results

are addressed in the last section.

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Chapter 2:

P. Generator

Model and

Main

11


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Characteristics

Chapter 2: P. Generator Model and Main

Characteristics

*he ,. generator converts the solar insulation into electric dc

po$er" t consists of an array of ,. cell modules connected in seriesC

parallel com'inations to provide the desired dc voltage and current"

*he terminal voltage current and the internal resistance of the array

depend on the num'er of series modules >s/ the num'er of

parallel modules >p/ and the insulation of the region $here the ,.

array is installed" *he appro3imate e


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ig"1! E


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ig"2! #odule constructed from @nA series cell"

ig"=! &n array constructed from >s series module and >p parallel

module"

*hree approaches are proposed in the design process for selecting

the ,. generator parameters" *hese approaches depend upon

determination the steady state operating point of the system

VPV

IPV

/ 7rstly and then maintaining this point on the photovoltaic

generator characteristics" n each approach another criterion should

'e taen into account in order to complete the design process and

o'tain the 7nal ,. generator characteristics "

n the 7rst approach the selection of the ,. generator parameters is

'ased on the motor starting current in addition to the system

operating point" n this approach taing the motor starting current

into account in the design process ensures the motor capa'ility for

starting $ith the rated condition *his results in adNusting the

1;


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re


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$here *am' is the am'ient temperature S is the solar insulation

and >8+* is the >ominal 8perating +ell *emperature "

in order to get .pv also in permissi'le range of design our cell

temperature must 'e 25 O+ as sho$n in a'ove e8+* is chosen 2: O+"

inally the third approach is demonstrating that *he ,. generator

output e


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>8+* 2: +

&ir mass ratio 1"5

,v )enerator $ors under standard test condition as mention in ta'le

F1G "*he rated condition of the load are 250. and 100& to meet this

demand $e select n >s and >p as mentioned in ta'leF2G"

*a'le 2! proper choices for design"

*a'le = ! ,. generator output for designed choices"

8% S>)E +E

Voc

./

Isc &/

0"5?6? =";. ma3

for #,,

ma3 for #,,

0"5 ="168% S>)E #8DUE

Voc Isc &/

1;";: =";Vm

./ for

#,,

Im &/ for #,,

12"5 ="16

8% U &%%&T sys/Voc ./ Isc &/ , at

Voc

1?

Selected for design numbe

rSeries cells in module n 25Series modules in array

>s

20

,arallel module in array

>p

=2


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JIsc /

2::"=5 10:":: 0VPV ./

for #,,

IPV &/

for #,,

, at #,,

/

250 101"12 252:0

ig"5! +urrent4voltage characteristics of the designed ,. array"

&pparently the output characteristic of the photovoltaic cells is

highly nonlinear" Using the #&*& instruction poly7t it is found

that a polynomial of the =0th order is accurate enough to represent

the output voltage as function of the current at full illumination as!

VPV=f(Ipv ) :/

$hereVPV is the terminal voltage of the &rray Ipv is the output

current"

*a'le ;!,oly7t curve 7tting coeVcients of the output characteristics of

the ,. generator at full solar irradiance"

1 K -1"5;?:21;==B;?52e-;B 2 K 1"=12=2;2:;511::e-;6

3 K 3.49690527921684e-44 4 K -2"0=5=B;2BB=22==e-;2

5 K 3.43027442425487e-39 6 K -B"0;6?6=B;=:;==5e-=?

1:


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7=1.14113392584619e-34

8 K--5"25==5;:;256B5:e-==

9 K 4.74273731326194e-31 10 K :"=:B??B5;?=01?1e-2B

11 K 4.46300440909447e-27 12 K?"=B1=:B?1?2=;20e-26

13

K5.83402290847196e-24 14

K1":6;;1?50BB;256e-22

15 K 2.29715581857733e-19 16 K -;"0B1666:66:66?1e-1?

17 K 3.37517907011393e-15 18 K 1.51793849065893e-13

19 K2"6?::6B0B2;==??e-12 20 K @.@/@B/C@/!?;!?e&

21 KW?"B1:12016==B;==eW0

B

22 K 2"=;:B?B:?600B15e-0?

23

K -="012=B12:=B2=16e-06

24

K 2.01588799987702e-05

25 K 0"001;?:=612;B0=5== 26 K -0"02652?=52=50;0B=

27 K 0"252:?2BB;26:5?6 28 K 1.34946000449467

29 K ="?=56=612BB05== 30 K &;.;BB@?C;??;??

31 K 2:B"56566?=65122

*a'le 5!,oly7t curve 7tting coeVcients of the output characteristics of

the ,. generator at 50X of full solar irradiance"

1 K -;"=1B60B;60=6?2Be-;0 2 K 1"?0;;=2026;:06Be-=?

3 K 2.72409400476518e-35 4 K 2"0:06?;6B0666=:e-==

5 K 5.00084117217477e-32 6 K -="50=51?601=?2:?e-=0

7=2.77771922634690e-28

8 K -6"15:B2600?5?2B0e-2?

9 K 1.66342273505569e-25 10 K -1"?12=21=622:5=Be-2=

1B


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11= 5"62B=:25;1==26=e-2=

12 K6"6?661;=6?60B?;e-20

13 K 2.12373395025036e-18 14 K-1"1=;B:6?25:5B;?e-16

15 K :"BB==2;60=650B6e-15 16 K -1"B6B1?65B26:B;:e-1=

17 K 2.23149090026853e-12 18 K 3.50038623381331e-10

19 K="0=1062;6;=;=;;e-0: 20 K &.44/4C//C@4Ce&!C

21= ="6B:B21:1B?61?5e-05 22 K

-0"000?06?66BB=2?2500

23 K 0"00B61=610;5::B;5? 24 K 0.0938333377710971

25 K0"6510605:?252=?= 26 K -="1=166:1BB05?11

27 K B"BB;?;062?005BB 28 K 19.7037302601006

29 K 21"266=;6;?0;1=5 30 K&!./?/B!4?B?

31 K 2:0"255=?5?55B65

ig"6! ,olynomial 7tted .4 characteristics of the designed ,. array

at t$o dierent illuminations"

20


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Cha+ter #!

DC-DCConverters

21


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Cha+ter #! DC-DC Converters

*o attempt the optimal point the D+ motor is matched to the solar

array 'y 'uc 'oost converter" *he three 'asic s$itching po$er

supply topologies in common use are the 'uc 'oost and 'uc-'oost" *hese topologies are non isolated i"e" the input and output

voltages share a common ground" *he po$er supply topology refers

to ho$ the s$itches output inductor and output capacitor are

connected" Each topology has uni


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a class of s$itched-mode po$er supplyS#,S/ containing at least

t$o semiconductors a diodeand a transistor/ and at least one

energy storage element a capacitor inductor or the t$o in

com'ination" ilters made of capacitors sometimes in com'ination

$ith inductors/ are normally added to the output of the converter to

reduce output voltage ripple"

ig": ! *he circuit con7guration of oost converter"

c/ uc-oost converter is a type of s$itched mode po$er supply

that com'ines the principles of the uc +onverterand the oost

converterin a single circuit" ,o$er supply designers choose the

'uc-'oost po$er stage 'ecause the output voltage is inverted

from the input voltage and the output voltage can 'e either

higher or lo$er than the input voltage" Ho$ever the output

voltage is opposite in polarity from the input voltage"*his chapter

descri'es steady state operation of the 'uc-'oost converter in

continuous-mode $ith ideal $aveforms given" :I

ig"B! +ircuit diagram of a 'ucC'oost converter

*he 'asic principle of the 'ucC'oost converter!

2=
https://en.wikipedia.org/wiki/Switched-mode_power_supplyhttps://en.wikipedia.org/wiki/Diodehttps://en.wikipedia.org/wiki/Transistorhttps://en.wikipedia.org/wiki/Capacitorhttps://en.wikipedia.org/wiki/Inductorhttp://www.learnabout-electronics.org/PSU/psu31.phphttp://www.learnabout-electronics.org/PSU/psu32.phphttp://www.learnabout-electronics.org/PSU/psu32.phphttps://en.wikipedia.org/wiki/Switched-mode_power_supplyhttps://en.wikipedia.org/wiki/Diodehttps://en.wikipedia.org/wiki/Transistorhttps://en.wikipedia.org/wiki/Capacitorhttps://en.wikipedia.org/wiki/Inductorhttp://www.learnabout-electronics.org/PSU/psu31.phphttp://www.learnabout-electronics.org/PSU/psu32.phphttp://www.learnabout-electronics.org/PSU/psu32.php


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hile in the 8n-state the input voltage source is directly

connected to the inductor /" *his results in accumulating energy

in " n this stage the capacitor supplies energy to the output

load"

hile in the 8-state the inductor is connected to the output

load and capacitor so energy is transferred from to + and %"

ig"10! *he t$o operating states of a 'ucC'oost converter"

+onceptual overvie$!

ie the 'uc and 'oost converters the operation of the 'uc-'oost

is 'est understood in terms of the inductors reluctance to allo$

rapid change in current" rom the initial state in $hich nothing is

charged and the s$itch is open the current through the inductor is

ero" hen the s$itch is 7rst closed the 'locing diode prevents

current from Yo$ing into the right hand side of the circuit so it must

all Yo$ through the inductor" 8ver time the inductor $ill allo$ the

current to slo$ly increase 'y decreasing its voltage drop" &lso

during this time the inductor $ill store energy in the form of a

magnetic 7eld":I

+ontinuous mode!

2;


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ig"11! aveforms of current and voltage in a 'ucC'oost converter

operating in continuous mode"

+ontinuous inductor current mode is characteried 'y current

Yo$ing continuously in the inductor during the entire s$itching

cycle in steady-state operation" f the current through the

inductor never falls to ero during a commutation cycle the

converter is said to operate in continuous mode" *he current and

voltage $aveforms in an ideal converter can 'e seen in igure FBG"

rom to the converter is in 8n-State so the s$itch S is

closed" *he rate of change in the inductor current K Ipv / is

therefore given 'y

B/

here .iK VPV, &t the end of the 8n-state the increase of is

therefore!

10/

D is the duty cycle" t represents the fraction of the commutation

period * during $hich the s$itch is 8n"During the 8-state the

s$itch S is open so the inductor current Yo$s through the load" f

25


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$e assume ero voltage drop in the diode and a capacitor large

enough for its voltage to remain constant the evolution of is!

11/

*herefore the variation of during the 8-period is!

12/

&s $e consider that the converter operates in steady-state

conditions the amount of energy stored in each of its components

has to 'e the same at the 'eginning and at the end of a

commutation cycle" &s the energy in an inductor is given 'y!

1=/

it is o'vious that the value of at the end of the 8 state must 'e

the same $ith the value of at the 'eginning of the 8n-state i"e"

the sum of the variations of during the on and the o states must

'e ero!

1;/

Su'stituting and 'y their e3pressions yields!

15/

*his can 'e $ritten as!

Vo= D

1DVpv 16/

rom the a'ove e3pression it can 'e seen that the polarity of the

output voltage is al$ays negative" &part from the polarity this

converter is either a 'oost converter $hen D is larger than 0"5 or a

'uc converter $hen D is lo$er than 0"5 or 'uer $hen D e


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2?


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Cha+ter $!

DC machines

Cha+ter $! DC machines

D+ machines are generators that convert mechanical energy to D+

electric energy and motors that convert D+ electric energy to

mechanical energy" #ost dc machines are lie ac machines in that

they have ac voltages and currents ithin them" Dc machines have

a dc output only 'ecause a mechanism e3ists *hat converts the

internal ac voltages to dc voltages at their terminals this#echanism is called a commutator"11I

2:


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*he real generators and motors do not move in a straight line they

rotate *he ne3t step to$ard understanding real dc machines is to

study the simplest possi'le e3ample of a rotating machine"11I

*he simplest possi'le rotating dc machine consists of a single loop

of $ire rotating a'out a 73ed a3is" *he rotating part of this machine

is called the rotor and the stationary part is called the stator"11I

*here $ere several reasons for the continued popularity of dc

motors" 8ne $as that dc po$er systems are still common in cars

trucs and aircraft" hen a vehicle has a dc po$er system it maessense to consider using dc motors" &nother application for dc

motors $as a situation in $hich $ide variations in speed &re

needed" efore the $idespread use of po$er e electronic recti7er-

inverters dc motors $ere une3celled in speed control applications"

Even if no dc po$er source $ere availa'le solid-state recti7er and

chopper circuits $ere used to create then necessary dc po$er and

dc motors $ere used to provide the desired speed control 11I"

*here are 7ve types of dc motors in general use!

a" Separately e3cited dc motor"

n this type of motors the armature and 7eld $inding are electrically

separate from each other" *he 7eld $inding is e3cited 'y a separate

D+ source"

ig"12! E


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'" Series dc motor"

n a series dc motor the 7eld $inding and armature $inding are

connected in series" *he 7eld $inding carries the same current as

the armature $inding" & series $ound motor is also called a

universal motor" t is universal in the sense that it $ill run e


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f 'oth series and shunt 7eld $indings are used the motor is said

to 'e compounded" n a compound machine the series 7eld

$inding is connected in series $ith the armature and the shunt

7eld $inding is connected in parallel" *$o types of arrangements

are possi'le in compound motors! +umulative compounding - f

the magnetic Yu3es produced 'y 'oth series and shunt 7eld

$indings are in the same direction i"e" additive/ the machine is

called cumulative compound" Dierential compounding - f the

t$o Yu3es are in opposition the machine is dierential

compound" n 'oth these types the connection can 'e either

short shunt or long shunt"

e" Shunt dc motor"

*he e


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*here are a fe$ variations and simpli7cations of this 'asic

e


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Since!nd K K

IA ,current & can 'e e3pressed as11I!

IA=!nd

K 2=/

com'ining the last t$o e


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ig"1?! *he magnetiation curve of Dc machine"

n this proNect $e choose a dc shunt motor $ith speci7c values for

EA VT

RA Rf

If IA / as follo$s!

& 50 hp 250 . 1200 rpm D+ shunt motor $ithout compensating

$indings has an armature resistance of 0"06\" ts 7eld circuit has a

total resistance %adN Z % of 50\ $hich produces a no-loads peedof 1200 rpm" *he shunt 7eld $inding has 1200 turns per pole" *he

armature reaction produces a demagnetiing mmf of :;0 &-turns at

a load current of 100&"12I

ig"1:! *he magnetiation curve of Dc shunt motor"

=;


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Speed +ontrol of Shunt D+ #otors11I!

1" &dNusting the 7eld resistance % and thus the 7eld Yu3/"

2" &dNusting the terminal voltage applied to the armature"

=" nserting a resistor in series $ith the armature circuit "

Chapter 5:

=5


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System

17uation

Chapter 5: System 17uations

n our ,roNect $e have mainly three parts! ,. +ells uc 'oost D+-

D+ converter and D+ shunt #otor"

=6


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ig"1B! ,. system con7guration"

Each one of them $as included in a single chapter" *his +hapter is

to sho$ the overall system of e


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#

2=

0"560B:01;2:B==;B

#3=

0"01B?;:===565;6:

y Su'stituting [25

] into [22

] !

VT K/ #1If2

Z #

2If+#3 Z IARA 26/

IT K

If Z IA

hereIT is the input current of the motor

If andIA are the

7eld and armature currents of the motor"

IT K

1DD

Ipv 2?/

*he motion e


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Chapter 6:

2umerical

Simulations

and 6esult

=B


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Chapter 6:2umerical Simulations and 6esult

0he numerical simulation results of the )* shunt motor and photovoltaic generator

are presented in this section.

*he steady-state output tor


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$ill increase the counter E# thus reducing current to the motor"

)radually the motor $ill reduce its speed" &s a result the D+ shunt

motoris capa'le of maintaining a constant speed irrespective of

load changes"

n case of D+ shunt motors $e can assume the field flu3 _ to 'e

constant" *hough at heavy loads _ decreases in a small amount

due to increasedarmature reaction" ut as $e are neglecting the

change in the flu3 _ $e can say that tor


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ig"22! *or


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&s much as the load increases the dra$n current from the motor $ill

'e increases too "n the other hand the voltage of the ,. generator

$ill decreases"

ig"2;! *or


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ig"26!*or


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Chapter 7:

Conclusions

;5


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Chapter 7:Conclusions

*he characteristics of the D+ shunt motor po$ered 'y ,. systemdue to 'uc 'oost D+-D+ converter at t$o dierent solar intensities

are studied" &ll parameters are in cascade com'ination $here ,.

system as a source and its cells are designed to provide their

ma3imum po$er at the rated conditions of the motor D+-D+

converter as a controller change its duty cycle to have 73ed output

voltage and Dc shunt motor as actuator" *he overall system has 7ve

varia'les Oa OO O OO $I $ith 7ve e


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A++endi8

*hese #atla' codes are used for dra$ing the designed and

polynomial 7tting curves of voltage-current characteristics of ,.

generator"

nK25` X of cells in module

#pK=2` Xparallel module

#sK20 `Xseries module

iscK=";`

isc2K=";42`

isatK6L10R-10/`

rpK6"6`

.K0!0"001!2::"=26B06:`

;?


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K#pLisc-isatLe3p=:"BL.4nL#s///-1/-.4#sLnLrp//`

i Kpoly7t.=0/`

.polyKpolyvali/`

Xplot.red.poly'lac/


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solve i/

vpa ans20/

vKans

.K0!0"001!2::"=26B06:`K#pLisc-isatLe3p=:"BL.4nL#s///-1/-.4#sLnLrp//`

Xplot./

format long

i Kpoly7t.=0/`

Xv Kpoly7tvi10/`

XKpolyvalvv/`

.polyKpolyvali/`

Xplot.red.poly'lac/

syms 3 32 3= 3; 35

Xbb31pv32if""""3=a""""3;D""""35

.pv Kpoly2symi/`

o K -

0"0=;260?15B2:?=BL32R2/Z0"560B:01;2:B==;BL32R1/Z0"01B?

;:===565;6:/ `

.o K 250`

ioK100`

1 K oL35 Z 0"06L3= -3;41-3;//L.pv`

2 K 3;41-3;//L.pv450 - 32 `

= K oL3=-1::"B`

; K 3;41-3;//L.pv/-.o `

5 K 3= Z 32 -3`

vpa11;/`

vpa21;/`

;B


50/53

vpa=1;/`

vpa;1;/`

vpa51;/`

solve12=;5/`pvKans"3

aKans"3=

fKans"32

DKans"3;

Kans"35

,.KD41-D//LaZf/

motorK1-D/4D/Lpv

#otorKaZf`

vpa,.;/

vpaa;/

vpaf;/

vpaD;/

vpa;/

nK25` X of cells in module#pK=2` Xparallel module

#sK20 `Xseries moduleiscK=";42`isatK6L10R-10/`rpK6"6`X-----7nding .ocsyms viK#pLisc-isatLe3p=:"BLv4nL#s///-1/-v4#sLnLrp//`solve i/vpa ans20/vKans.K0!0"001!2?B"0B626B5`

K#pLisc-isatLe3p=:"BL.4nL#s///-1/-.4#sLnLrp//`Xplot./

50


51/53

format longi Kpoly7t.=0/`Xv Kpoly7tvi10/`XKpolyvalvv/`.polyKpolyvali/`Xplot.red.poly'lac/

syms 3 32 3= 3; 35

Xbb31pv32if""""3=a""""3;D""""35

.pv Kpoly2symi/`o K -

0"0=;260?15B2:?=BL32R2/Z0"560B:01;2:B==;BL32R1/Z0"01B

?;:===565;6:/ `.o K 250`

ioK100`

1 K oL35 Z 0"06L3= -3;41-3;//L.pv`

2 K 3;41-3;//L.pv450 - 32 `

= K oL3=-:2"6?` X:2"6? ma3

; K 3;41-3;//L.pv/-.o `

5 K 3= Z 32 -1-3;/43;/L3`

vpa11;/`vpa21;/`vpa=1;/`vpa;1;/`vpa51;/`

solve12=;5/`

pvKans"3aKans"3=fKans"32DKans"3;Kans"35,.KD41-D//LaZf/motorK1-D/4D/Lpv#otorKaZf

51


52/53

6eferences

'( Allan D. Hambley% Electrical Engineering ,rinciples and Applications% C thedition%

/!;.

[2I aughton #"&" and arne D Electrical Engineers %eference

oo 16thEdition 200="

'4( . Michael Mooney% AD* ,ress of *ane Hill% A self&study guidebook on the

e$citing world of solar electricity%@@.

';( Dobert . Erickson and )ragan Makshnovic % 9undamental of ,ower

Electronics % #econd Edition %


53/53

6I %ashad EE# Shoralla SS ,. system fed D+ motor controlled 'y

'oost converter 1BBB"

?I Daniel " Hart ntroduction to ,o$er Electronics >e$ ersey

US& 1BB? "

:I>ed #ohan*ore #" Undeland illiam ,"%o''ins ,o$erElectronics! +onverters &pplications and Design 200="

BI )il'ert #" #asters

%ene$a'le and EVcient Electric ,o$erSystems200;"

10I Stephen +hapman Electric #achinery undamentals 5th Ed

2012"
https://www.google.jo/search?hl=ar&tbo=p&tbm=bks&q=inauthor:%22Ned+Mohan%22https://www.google.jo/search?hl=ar&tbo=p&tbm=bks&q=inauthor:%22Tore+M.+Undeland%22https://www.google.jo/search?hl=ar&tbo=p&tbm=bks&q=inauthor:%22William+P.+Robbins%22https://www.google.jo/search?hl=ar&tbo=p&tbm=bks&q=inauthor:%22Ned+Mohan%22https://www.google.jo/search?hl=ar&tbo=p&tbm=bks&q=inauthor:%22Tore+M.+Undeland%22https://www.google.jo/search?hl=ar&tbo=p&tbm=bks&q=inauthor:%22William+P.+Robbins%22

pv powered dc motors design and analysis

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