Transcript ENT 163 08-08 - UniMAP Portal

FUNDAMENTALS OF ELECTRICAL
ENGINEERING
[ ENT 163 ]
LECTURE #8
INTRODUCTION TO AC CIRCUITS
HASIMAH ALI
Programme of Mechatronics,
School of Mechatronics Engineering, UniMAP.
Email: [email protected]
CONTENTS
•
•
•
•
•
Introduction
Sinusoids
Phasors
Impedance and Admittance
AC Power Analysis
IMPEDANCE AND ADMITTANCE
Element
Impedance
Admittance
R
Z=R
Y=1/R
C
Z=jωL
Y=1/jωL
L
Z=1/jωC
Y=jωC
•
When ω=0 (dc source), ZL=0 and Zc=∞ (confirm- inductor acts like short
circuit, capacitors acts like open circuit).
•
When ω=∞ (high frequencies ) ZL= ∞ and Zc=0 (indicate- inductor acts
like open circuit, capacitors acts like short circuit).
IMPEDANCE AND ADMITTANCE
Impedance in rectangular and polar form:
R  Z cos 
Z  R  jX  Z 
X  Z sin 
Z  R2  X 2
  tan 1
X
R
Admittance: Y the reciprocal of impedance, measured in Siemens (S)
Y
1 I

Z V
As complex quantity:
Y  G  jB
Where,
G  jB 
G
1
R  jX
R
X
,
B


R2  X 2
R2  X 2
IMPEDANCE COMBINATIONS
Consider the N series-connected impedances:
1. The same current will flows through the impedance; applying KVL
V  V1  V2  ...  VN  I(Z1  Z 2  ...  Z N )
The equivalent impedance:
Z eq  Z1  Z 2  ...  Z N
For N=2,
Z1
Z2
V1 
V, V2 
V,
Z1  Z 2
Z1  Z 2
IMPEDANCE COMBINATIONS
Consider the N parallel-connected impedances:
 I1 I 2
IN

I  I1  I 2  ...  I N  V 
 ... 
ZN
 Z1 Z 2
For N=2,
Current in the impedances are:
Z2
Z1
I1 
I, I 2 
I
Z1  Z 2
Z1  Z 2



IMPEDANCE COMBINATIONS
Delta-wye circuit
The delta-to-wye transformation
IMPEDANCE COMBINATIONS
The Conversion Formulas are as Follows:
Y-∆ Conversion
Za 
Z1Z 2  Z 2 Z 3  Z 3Z1
Z1
Z1Z 2  Z 2 Z 3  Z 3Z1
Zb 
Z2
Z1Z 2  Z 2 Z 3  Z 3 Z1
Zc 
Z3
For a ∆-Y balanced circuit:
Z∆=3ZY
∆-Y Conversion
Zb Zc
Z1 
Z a  Zb  Zc
ZcZa
Z2 
Z a  Zb  Zc
Z a Zb
Z3 
Z a  Zb  Zc
AC POWER ANALYSIS
• Power analysis- important-usage in electric utilities.
Instantaneous power (in Watts) is the power at any instant of time.
p(t)=v(t)i(t)
Average power (in Watts) is the average of the instantaneous power
over one period.
P=S cos(θv-θi)
• A resistive load (R) absorbs power at all times, while reactive
load (L or C) absorb zero average power.
Apparent power (VA) is the product of the rms value of voltage and
current
S=VrmsIrms
IMPEDANCE COMBINATIONS
Reactive power (Var) is the power kept by reactive elements (L and C)
Q=S sin (θv-θi)
Power factor is the cosine of the phase difference between voltage and
current, or the cosine of the angle of the load impedance.
Power factor= P/S = cos (θv-θi)
Further Reading
Fundamentals of electric circuit. (2th Edition), Alexander, Sadiku, MagrawHill.
(chapter 9&11).
Electric Circuits.(8th edition), Nilsson & Riedel, Pearson. (Chapter 9).
5  j 2
+
-
+
A
1100
110  240
+
10  j8
110 120
10  j8
5  j 2
5  j 2
B
C
10  j8