basic concepts presentation
TRANSCRIPT
-
7/31/2019 Basic Concepts Presentation
1/45
Ontoseno Penangsang1)
1) Electrical Department, Sepuluh Nopember of Institute TechnologySurabaya, 60111, Indonesia
-
7/31/2019 Basic Concepts Presentation
2/45
Single Phase Circuits
Review of Phasors
Real and Reactive PowerReal and Reactive Loads
Power Triangle
Real and Reactive Power
FlowOntoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
3/45
Review of Phasors
Goal of phasor analysis is to simplify theanalysis of constant frequency ac systems
v(t) = Vmax cos(wt + qv)i(t) = Imax cos(wt + qI)
Root Mean Square (RMS) voltage of sinusoid
2 max
0
1( )
2
TV
v t dt T
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
4/45
Phasor Representationj
( )
Euler's Identity: e cos sin
Phasor notation is developed by rewriting
using Euler's identity
( ) 2 cos( )
( ) 2 Re VV
j t
j
v t V t
v t V e
q
w q
q q
w q
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
5/45
PhasorRepresentation, contd
Then drop the constant terms
( ) Re 2
V cos sin
I cos sin
VjV
j t
V V
I I
V V e V
v t Ve
V j V
I j I
q
w
q
q q
q q
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
6/45
Advantages of Phasor Analysis
0
2 2
Resistor ( ) ( )
( )Inductor ( )
1 1Capacitor ( ) (0)
C
Z = Impedance
R = Resistance
X = Reactance
XZ = =arctan( )
t
v t Ri t V RI
di tv t L V j LI
dt
i t dt v V I j C
R jX Z
R X
R
w
w
Device Time Analysis Phasor
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
7/45
Sine Wave Basics
RMS a method for computing the effective valueof a time-varying e-m wave.
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
8/45
Real, Reactive and ApparentPower in AC Circuits
in DC circuits: P=VI but= in AC circuits: averagepower supplied to the load will be affected by thephase angle q between the voltage and the current.
If load is inductive the phase angle (also calledimpedance angle) is positive; (i.e, phase angle ofcurrent will lag the phase angle of the voltage) andthe load will consume both real and positive reactivepower
If the load is capacitive the impedance angle will benegative (the phase angle of the current will lead thephase angle of the voltage) and the load willconsume real power and supply reactive power.
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
9/45
Resistive and Reactive Loads
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
10/45
Impedance Angle, CurrentAngle & Power
Inductive loads positive impedanceangle, current angle lags voltage angle
Capacitive loads negative impedanceangle, current angle leads voltage angle
Both types of loads consume real powerOne (inductive) consumes reactive as
well while the other (capacitive) suppliesreactive power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
11/45
Real and Reactive PowerEquations
First term is energy flow into the circuit Average =
Real power (P)
Second term is power transferred back and forthbetween source and load (Reactive power Q)
v(t) = 2 V cos t
i(t) = 2 I cos (t-)
p(t) =v
(t)i(t) = 2VIcos t cos (t-
)
p(t) = VI cos(1 + cos 2t) + VI sinsin (2t)
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
12/45
Real term averages to P = VI cos (+)
Reactive term (amplitude) to Q = VI sin
(+/-)
Reactive power is the power that is first stored and thenreleased in the magnetic field of an inductor or in the
electric field of a capacitor
Apparent Power (S) is just = VI
Apparent PowerEquation
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
13/45
Voltage, Current and Poweras a function of time
Voltage
Current(lagging)
Power
Real Power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
14/45
Voltage, Current and Poweras a function of time
Voltage
Current(in phase)
Power
Real Power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
15/45
Voltage, Current and Poweras a function of time
Voltage
Current(lags 90%)
Reactive Power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
16/45
Loads withConstant Impedance
V = IZ
Substituting into real and reactive powerequations
P = I2Z cos q Q = I2Z sin q
S= I2Z
Since Z = R +jX = Z cos q + jZ sin q P = I2R and Q = I2X real and
reactive power consumed by load
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
17/45
Complex Power andKey Relationship ofPhase Angle to V&I
S= P + jQ
S= VI(complex conjugate operator)
If V= V30o and I= I15oTHEN.. COMPLEX POWER SUPPLIED TO
LOAD :
S= (V30o)(I-15o) = VI (30o-15o )
= VI cos(15o ) + jVI sin(15o )
NOTE: Since Phase Angle q = qv - qiS= VI cos(q) + jVI sin(q) = P + jQ
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
18/45
S= P + jQ
S= VI cosq + j VI sinq
S= VI(cosq + j sinq)
S= VIej OR S=VIq
Since V= V00 and I= I-q
S = VI*
V0
I-q
q
Complex Power
Ontoseno [email protected]
i
-
7/31/2019 Basic Concepts Presentation
19/45
Review V, I, Z
If load is inductive then the Phase Angle(Impedance Angle Zqo) is positive, Ifphase angle is positive, the phase angleof the current flowing through the loadwill lag the voltage phase angle acrossthe load by the impedance angle Zqo.
0
0
0
Z
V
Z
0V
Z
VI
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
20/45
The Power Triangle
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
21/45
Real Power Flow
0VV
q II
qcosIq
V
I
If the component of I along the axis of E is in phase with E, thepower is generated powerwhich is being deliveredto the system,for this component of current is always flowing away from the
positively marked terminal
P, the real part of VI* (Vicos), is positive.
The Source is a Generator
System
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
22/45
q II
0VVqcosI
V
I
q
System
If the component of current along the axis of E is negative (1800 outof phase with E), power is being absorbed
P, the real part of VI* (Vicos), is negative.
The Source is a Motor
Real Power Flow
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
23/45
Reactive Power Flow
0VV
90II
V
I90
LX
Positive reactive power equal to |I|2X is supplied to the inductancesince inductance draws positive Q.
Q, the imaginary part of VI* (Visin), is positive
I lags V by 900
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
24/45
Reactive Power Flow
q II
0VV V
I90
Negative Q must be supplied to the capacitance of the circuit, orthe source with the emf E is receiving positive Q from the capacitor
Q, the imaginary part of VI* (Visin), is negative
I leads V by 900
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
25/45
Example
V = 1200o V
Z = 20-30o
Calculate current I, Power Factor (is itleading or lagging), real, reactive,
apparent and complex power suppliedto the load
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
26/45
Three-Phase (3- ) Circuits
What are they?
Generating 3- Voltages andCurrents
Balanced systems
Wye (Y) and delta () connectionsThree Phase Power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
27/45
What does Three-Phase mean?
A 3- circuit is a 3- AC-generation
system serving a 3- AC load
3 - 1- AC generators with equal voltagebut phase angle differing from the
others by 120o
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
28/45
Ontoseno [email protected]
One Cycle (1/50th sec.)
-
7/31/2019 Basic Concepts Presentation
29/45
Common Neutral
A 3- circuit can have the negativeends of the 3- generators connected to
the negative ends of the 3- AC loadsand one common neutral wire cancomplete the system
If the three loads are equal (orbalanced) what will the return current bein the common neutral?
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
30/45
If loads are equal.
the return current can be calculated tobe
ZERO!
Neutral is actually unnecessary in abalancedthree-phase system (but isprovided since circumstances maychange)
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
31/45
BalancedThree Phase Systems
Balanced
Same amplitude
120phase diff.
Phase shift
ia lags ua angle
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
32/45
Three-phase currents
Balance: Ia+ Ib+ Ic=0
No return current Losses reduced
No return conductor
a
b
c
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
33/45
Wye (Y) connection
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
34/45
Wye (Y) connection
Ic
Ia
Ib
a
LOADSOURCE
a
bb
c c
nn
n : neutral
Vab = Vbc = Vca = VL : line to line voltage
Van = Vbn = Vcn = Vp : line to neutral (phase) voltage
Ic
Ia
Ib
Ia = Ib = Ic = IL : line current
= Ip : phase current
Ontoseno [email protected]
V l C
-
7/31/2019 Basic Concepts Presentation
35/45
Voltage CurrentRelationships
IL = Ip
VL = 3 VpVL, Vp, IL , Ip : rms values of
voltage and current
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
36/45
Phasor Diagram
SOURCE = LOAD
Vab
30o
opcn 120VV
opan 0VV
o
pbn VV 120
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
37/45
Delta ( ) connection
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
38/45
Delta ( ) connection
Ic
Ia
Ib
SOURCE
ab
c
Vab = Vbc = Vca = VL : line to line voltage
= Vp : phase voltage
Iab
Ibc
Ica
Ic
Ia
Ib
LOAD
ab
c
Iab
Ibc
Ica
Iab = Ibc = Ica = Ip : phase current
Ia = Ib = Ic = IL : line current
Ontoseno [email protected]
V lt C t
-
7/31/2019 Basic Concepts Presentation
39/45
Voltage CurrentRelationships
VL = Vp
IL = 3 IpVL, Vp, IL , Ip : rms values of
voltage and current
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
40/45
o
pbc II 120
o
pca II 120 bI
opab II 0
o30
o
pbc II 120
o
pca II 120
o
pab II 0
aI
o30
Phasor Diagram
SOURCE LOAD
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
41/45
=uiR
=uiL
Three Phase Power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
42/45
Three Phase Power
pa(t) , pb(t) , pc(t) : phase power
ptotal(t)= pa(t)+ pb(t)+ pc(t)
three phase power
pa(t) = pb(t) = pc(t)
If voltages and currents balanced
cosj need not be zero
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
43/45
ppp
ppp
SinIVQ
CosIVP
j
j
j
j
3
3
3
3
FOR A BALANCED THREE PHASE SYSTEM :
p : phase angle between
phase voltage and phase
current (lagging)
Three Phase Power
THREE PHASE POWER : 3 X PHASE POWER
Watt : real power
Var : reactive power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
44/45
Rumus Daya 3 Fasa
pLL
pLL
SinIVQ
CosIVP
j
j
j
j
3
3
3
3
Three Phase Power
LpL
p IIV
V ;3
3; LpLp
IIVV
For Y connection
For connection
Watt : real power
Var : reactive power
Ontoseno [email protected]
-
7/31/2019 Basic Concepts Presentation
45/45
LLIV
QPS
3
22
VA
Three Phase Power
APPARENT POWER :