2. AC Circuits.ppt
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Transcript of 2. AC Circuits.ppt
1
Review of AC Circuits
Smith College, EGR 325March 27, 2006
2
Objectives
• Power calculations and terminology
• Expand understanding of electrical power – from simple linear circuits to
– a high voltage power system
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
4
ac Waveform
t
v Vmax
waveform theoffrequency theis
2
f
f
tsinVv max
5
How AC is Generated
Stator
Windings
N
S
Rotor
6
Angle
v
X
N
S
f 900
1800
2700
3600
How AC is Generated
7
t
v
sec/3772
sinmax
radf
tVv
2
VVV max
rms
AC Phasor Representation
8
)(sin
sin
max22
max11
tVv
tVv
V1
V2
22
11 0
VV
VVt
v1v2
Reference
9
)(cos
cos
max22
max11
tVv
tVv
V1
V2
22
11 0
VV
VVt
v1v2
Reference
10
Phasors
tj
mj
m
etv
VeV
V
V
Re)(1
11
Representing Power
12
Power Calculations
• P = VI
• P = I2R
• P = V2/R
• S = VI
• S = I2Z
• S = V2/Z
13
Resistance Impedance
• Resistance in • Capacitance in F
• Inductance in H
• Z = R + jX
14
Instantaneous Electric Power [p(t)]
)sin()(
)sin()(
max
max
tIti
tVtv
])2cos()[cos(2
)( maxmax tIV
t
Fixed average Zero average
V
I
)sin()sin()(*)()( maxmax ttIVtitvt
15
Instantaneous vs. Average Power
)2cos(2
1)cos(
2
1)( ivmmivmm tIVIVtp
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
17
Real & Reactive Power – Time Domain
])2cos()[cos(2
)( maxmaxvivi t
IVtp
t
Q(t)
)()( tQPtp
t
p
18
Complex Power
*IVS
sincos IVjIVS
VIIVIVS 0*
V
I
IMPORTANT is the power factor angle
QjPS
II
Real Power Reactive Power
19
Example: Current Flow
20
Example: Power Flow
21
Power System Operations
22
Operating Challenges
• Load is stochastic and is not controlled
• Power flows cannot be directed or controlled
• Electricity cannot be stored
• Everything happens in real-time
• Generation can be controlled
23
Power System Variables
• Generators produce complex power– S = P + jQ– Real power, P, able to perform useful
work – Reactive power, Q, supports the system
electromagnetically
• Single system frequency, f
• Voltage profile, V
24
Real Power Flow – Voltage Relation
Power (pu)
Vo
ltag
e (p
u)
• In normal system operation, frequency/real-power dynamics are decoupled from voltage/reactive-power
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
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 disconnect
generators– Operators may disconnect regional tie lines
27
Reactive Power Analogy
• Voltage and reactive power allow real power to flow
• Reactive power – Energy stored in capacitance and inductance– Supports the electromagnetic fields along
transmission lines– Cannot be transmitted long distances
• Analogy– Inflatable water pipes
28
Voltage Collapse
• The real power demanded is above the transfer capability of a transmission line
• Return to the water pipe analogy– Load draws too much power – dips into the
stored reactive power – “collapses” the pipe
• Equations: P = V*I, I = V/Z– Load wants more power: Decrease apparent
impedance (Z), to increase current draw (I), which allows increased P
– But, if P at limit, result is to decrease V
29
Power (pu)
Vo
ltag
e (p
u)
Real Power Flow – Voltage Relation
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