Handwritten Complete notes for Electromechanical Design Systems

e- Electro Mechanical Systems -
in
ELECTRONICS

AC power VP - - - - - -
- - -
- - - - - - - - -




parallel circuits 7- =¥=¥+¥

✓
- - -

•




-




=z,=(RpXi=£R÷÷
{
Vac=Vpsin(wt to /
<T=¥=¥i
→
Phase
,
ang ,
×,
Rp ,
,× ,
& >
Peak voltage angular
=
RpXi+jR = Rs +jXs
frequncyw -2nF
-
-




1
.
,
Rp + y,



×s=RP
•
Euler's Identity Asm(wt±0)=Acos4±jAsino Rs
mm


Xs
where
,
Rs
__p?¥÷ ,
Rp
-
+ Xu

= Ae -50
A-sink a
•
AC Phasors

9
'




i. Ac circuits
G. < 1) (Zich ) (2,2-2)<(0,1-02)
•

-_




Acosol Inductance :
Zc=jwL
2-1<0 ⇐
j=f1 -
,
= < (0 -1oz) ,




⇒
Zz
Capacitance -2C Zz< Oz
-
: -




( jczisino )
(£10S i
+
Zzcos 2) ±

Z ,< 01, ± zz< Oz
=


Complex Impedances .
+ Zzsinoz )

Impedance
•
Real Power
by
.




voltage is
phase shifted 90
mm
ipsin ( wt)
"


¥2 P=✓PP=Vrms
I,

Irms==¥
-
-
a



Z<=jwL gao
'




Vrms
-

-
-

Irms


i"""i
"
¥
vi. L%i=wLsin(wt+ao
-




)
•
Inductors have no real power i=t / Vdt
Inductance tags Vpsinwt
Vpcoswtdt
current
•

.
i =
=


=L
Capacitance
'




Current is
phase shifted by 90
•
-

T




t÷]
'
→ + VP P=O
÷ /ride
p= F- ⇒

Zc=¥c V, =
Vpsincwt )
qao
'




o
*
o




Average Power
tfidt
i""i
capacitor =0
•
>
ve of v.


ic=Cd¥= wcvpsincwttao) v.
E) ipcoswtdt =
iPsY
IT
¥ /Cipcoswt) (ipsin¥)at
Capacitance Current
p=÷ /
lags voltage
•



v. i ⇒ P= -




Series circuits
,
•

o




Impedance •


Complex Power
R
Zu=R+jXu Qu Qi
L
✗ < =wL to
=¥¥
- -
-




i=Ip④
my
/
-




phrase
↳



(E)
Phase angle

Ft
Load
/ f-
' of
2- angle of

to
-

current
tan ~
angle
-




voltage
-




-




IrmsZZ=Irm}R+jIrmsX
n




Tt
Z-,=fFÑ jx
'



i:*
Z

nor s P+jQ
=



10 i 2- =R+jX
R
2-+ =/ 2- IE 5- Irons'Z
* s=P+jQ⇒1slL =
Complex Power (VA)
①
F- Irons'R= Active Power ( w )
capacitors 2-
⇐
= Rt = R -

jXc Xc= ¥ so
p
Is / =fF+F
Q= Irmix Reactive Power (Vars)
=



R a 1st Apparent Power
-




12-1 Fix q=tmif¥) R=Zcos X 2-Sino :
P Nrmsllirmslcoso
- -
- -
-
-




5- I. i. i. =/Irmslti Q= / Vrmsl / Irmslsino

Ze=ÑtÉ¥)
R
lvrmsllov S lvrmslttrms / €0T
-




vi.
-



s .




10
¥zcos(wt+Qv)
"

Xc =

z i.
E- =/ 2- I -10L
,

, e- Electro Mechanical Systems -
in



• Power Factor Correction
Star & Delta Connected
Systems
•




•
Aim to the 4 close to
possible
get as zero as
,



ie it as close to 1
STAR
.


get as possible .




Positive sequence

c) { L
Z'Z Irms =
"
Z,
✗ ¥ ,
vpna=Vph Lo
'
Phase current

/
=

-2 +
Zz Line current
Vpn £120
ng yn
'




Vpn ,
,
=

VA
n •
Line
voltage
IF ,= cog ( ) Vpn -4240 phase
whatever Vpnc
to
'


-1 -
-




voltage
g- LVB
value
-2 Zz
VAB=ÑVPnÉ
,


Qc=Q Qi
-




Negative
•
each
g-
s

¥÷↳o
Q terminal is connected Vph =
.




QIQ ,
Q1= tan ,
=
to neurone .




-




P
Vpn lags thine by 30


{
÷÷÷
'




Xc =
✗<=




;µ☐|
Mine =/ 73'
✗
Vpn
IF ""
•
VAB
•
Resonant Circuits Negative sequence
⇒ 1 Phase Current

Zc=÷wc Vpha Vpn Lo
=


Zc=jwL
-

•
m_ =
☐
r a < Line current
VphB Vpn -440
=


Phase
voltage Voltage in
•




[WL ⇒
-




⇒
Z Rt Vpnc Vpn -420
=
-


=
, ; each phase
LT Line between VaB=BVph3L°
Rtjxc jxc voltage Voltage
:
ZT
•
-_ -




Resonant
frequency occurs
£0
lines
Vpn
=

⇒ circuit
.




ZT
purely
at Resonant when is real
frequency Phase Current
•



Current
flowing
•
:
in

⇐ =p Is/=p pF=1 dissipates only real Power .




Vpn
⇒
leads thine
'



30
ZZ
each
phase .


by
R L
Zz =/ 73
Nine Vpn
, '
✗

C R , ~
~ m,




DELTA
T
~

IT
}
~
2- a rz
Positive Sequence
,




Vpna
'


VB
=
VAB
Phase
voltage
w=[÷F w=€¥ ,
%
a
VpnB= VBC
vpnc
-

.
vac
Line
voltage
=




-

it
Phase current
Ica Ipnc
-




Inna
3 Phase
Systems ftp.hB-T-LBI-IpnA
-
- +

→ ve
Line
Current


Ipnc =
Inc +
IpnB
Negative terminal
•



g. each




an
Va Va Vpnasecoslwt) "
'



ee
is connected
-




to positive
~



IphA=IpnL0
-



a Ipna=

÷ Ica →
•
A
- IphB= Ipn °
'




Vpna =
VAB
FT


ÑÉ|•Bµ
-
✓B
Vpnasecoscwt ) Iphc =
Iph # °
"Iune

<24"
vb Vb -120
f Ipn
q -1.73 ✗
~




⇐ ""
-
- -




""☐ "
✓ Ipn leads Ione by
'




Ip#
30
•




,


Vpnasecoslwt -240 )
, +
Vc Vc
-




¥3
-

~




/ VAT
-
-




Vc
Negative sequence
→

Inc
% -




Positive Phase -

Rotates anticlockwise
→
Iea=IpnA Ipnc -




Ipn __ to

Phase
voltage Voltage in
IphB=Iph-440
.




✗ phase .fr/--/VpnaseBl--/VphasecI
-




ava Trine -173 ✗ Ipn
-

.



no
Ipnc Ipntzo
.



each
phase =


Y '

Tno
Phase
voltage
/ Ia / =/ Ipd =/ Ic /
.




Line Voltage -




voltage flowing
line Frottage
'
Vrs in each line
star :
Delta :

Phase current Current flowing
ABC
sequence Va Vpncos (wt d)
: -



+
-
-




"s
each phase
Vpn
in

V☐= Vpncos (wt ¢-120 ) Ipn
=
+ =




Vc =
Vpn cos (wt to -240 ) Vpn Uh
Ipn I,
-_
-_