Review of AC Circuits
-
Upload
electrotecnia2732 -
Category
Documents
-
view
227 -
download
0
Transcript of Review of AC Circuits
-
8/13/2019 Review of AC Circuits
1/30
1
Review of AC Circuits
Smith College, EGR 325
March 27, 2006
-
8/13/2019 Review of AC Circuits
2/30
2
Objectives
Power calculations and terminology
Expand understanding of electrical
power from simple linear circuits to
a high voltage power system
-
8/13/2019 Review of AC Circuits
3/30
3
Overview
Basic Circuits Sinusoidal waveform representation
Root mean square
Phase shift Phasors
Complex numbers
Complex impedance
Electric Power Complex: real & reactive power
Power factor and power factor correction
-
8/13/2019 Review of AC Circuits
4/30
4
ac Waveform
t
vVmax
wavefortheoffrequencytheis
2
f
f
tsinVv max
-
8/13/2019 Review of AC Circuits
5/30
5
How AC is Generated
Stator
Windings
N
S
Rotor
-
8/13/2019 Review of AC Circuits
6/30
6
Angle
v
X
N
S
f 900
1800
2700
3600
How AC is Generated
-
8/13/2019 Review of AC Circuits
7/30
-
8/13/2019 Review of AC Circuits
8/30
8
)(sin
sin
max22
max11
tVv
tVv
V1
V2
22
11 0
VV
VVt
v1 v2
Reference
-
8/13/2019 Review of AC Circuits
9/30
-
8/13/2019 Review of AC Circuits
10/30
10
Phasors
tjm
jm
etv
VeV
V
V
Re)(1
-
8/13/2019 Review of AC Circuits
11/30
11
Representing Power
-
8/13/2019 Review of AC Circuits
12/30
12
Power Calculations
P = VI
P = I2R
P = V2/R
S= VI
S= I2Z
S= V2/Z
-
8/13/2019 Review of AC Circuits
13/30
13
ResistanceImpedance
Resistance in
Capacitance in F
Inductance in H Z = R +jX
-
8/13/2019 Review of AC Circuits
14/30
-
8/13/2019 Review of AC Circuits
15/30
15
Instantaneous vs. Average Power
)2cos(2
1)cos(
2
1)( ivmmivmm tIVIVtp
-
8/13/2019 Review of AC Circuits
16/30
16
Instantaneous vs. Average Power
)2cos(
2
1)cos(
2
1)( ivmmivmm tIVIVtp
Instantaneous power is written as
The average of this expression is
)cos(2
1ivmmIVP
-
8/13/2019 Review of AC Circuits
17/30
17
Real & Reactive PowerTime Domain
])2cos()[cos(2
)( maxmax vivi tIV
tp
t
Q(t)
)()( tQPtp
t
p
-
8/13/2019 Review of AC Circuits
18/30
-
8/13/2019 Review of AC Circuits
19/30
19
Example: Current Flow
-
8/13/2019 Review of AC Circuits
20/30
20
Example: Power Flow
-
8/13/2019 Review of AC Circuits
21/30
21
Power System
Operations
-
8/13/2019 Review of AC Circuits
22/30
-
8/13/2019 Review of AC Circuits
23/30
-
8/13/2019 Review of AC Circuits
24/30
-
8/13/2019 Review of AC Circuits
25/30
25
Real Power and Frequency
P and f dynamics are coupled Demand > Supply: frequency will decrease
(more energy drained from system than produced,
acts like brakes on the turbines)
Supply > Demand: frequency will increase(more energy in the power system than consumed,
acts like an accelerator so turbines spin faster)
Generation-based frequency regulation Generator inertia
Generator governors
-
8/13/2019 Review of AC Circuits
26/30
26
Frequency Problems
Imbalances in supply and demand beyond
the capabilities of these generator controls
Load may be dropped, or shed by operators
Equipment protection may disconnectgenerators
Operators may disconnect regional tie lines
-
8/13/2019 Review of AC Circuits
27/30
-
8/13/2019 Review of AC Circuits
28/30
28
Voltage Collapse
The real power demanded is above thetransfer capability of a transmission line
Return to the water pipe analogy
Load draws too much powerdips into thestored reactive powercollapses the pipe
Equations: P = V*I, I = V/Z
Load wants more power: Decrease apparentimpedance (Z), to increase current draw (I),
which allows increased P
B u t, if P at limit, result is to decrease V
-
8/13/2019 Review of AC Circuits
29/30
29
Power (pu)
Voltage(pu)
Real Power FlowVoltage Relation
-
8/13/2019 Review of AC Circuits
30/30
30
Power System Response to Outages
Power flows on the paths of least
impedance
As elements are removed (fail), the
impedance changes and so power flows
change Instantaneously
Human and computer monitoring of and
reaction to problems is on a much slower
timescale