Transcript 150LECTURE9POWERINACCIRCUITS Lecture Notes Page

FOWLER CHAPTER 9
LECTURE 9 POWER IN AC
CIRCUITS
POWER IN RESISTIVE CIRCUITS, CHAP 9
WITH A RESISTIVE LOAD, CURRENT AND VOLTAGE ARE IN PHASE. F.9.1
THIS COULD BE AN ELECTRIC HEATER, STOVE, LAMP ETC.
Ac source drives a purely resistive load.
V
I
In a purely resistive circuit, all circuit power is dissipated by the
resistor(s). Voltage and current are in phase with each other.
2
V
P  IV  I 2 R 
R
+POWER= (-CURRENT)X(-VOLTAGE)
RESISTORS
POWER IN OUT OF PHASE CIRCUITS
REACTANCE IS LIKE RESISTANCE IN AC CIRCUITS
WHICH INCULDES CAPACITORS AND INDUCTORS.
CAPACITORS
INDUCTORS
THERE IS NO EASY WAY TO CALCULATE POWER WHEN PHASE SHIFTS OCCUR.
WHEN CURRENT AND VOLTAGE ARE OPPOSITE; (Neg. or pos.) voltage times (Neg. or
pos.) current = - power
  
  
WHAT DOES NEGETIVE POWER MEAN?
POWER IS FLOWING BACK FROM THE LOAD TO THE SOURCE.
WITH A 90° PHASE SHIFT, NO POWER IS USED BY REACTIVE COMPOENTS,
ONLY RESISTANCE USES POWER.
POWER IN RESISTIVE, REACTIVE CIRCUITS CAN BE FOUND FROM,
P =IVCOSØ
FOR RESISITANCE ONLY CIRCUITS: Ø = 0, SO COS(0°) = 1
THEN P= IV(1) =IV
IT
COSØ =IR/IT
Ø
IR
COS IS A MATH FUNCTION THAT CAN VARY FROM 1 TO 0
FOR A ANGLE IN DEGREES FROM 0° TO 90°.
FOR RESISTIVE CIRCUITS ONLY: LOAD
CURRENT AND VOLTAGE ARE IN PHASE.
IN A CIRCUIT WITH CAPACITANCE ONLY: I LEADS V BY 90º
IN A CIRCUIT WITH INDUCTANCE V LAGS I BY 90º
If a sinusoidal voltage is applied to an resistive circuit with a phase
angle of 0o, the resulting voltage and current waveforms will look
like this
Given that power is the product of voltage and current (p =
i v), let’s look at the waveform for power in this circuit.
If the power waveform is plotted for a resistive AC circuit, it will look like this
V
Circuit with a capacitor current leads voltage.
Circuit with a inductor voltage leads current.
+
-
Power
+
Power
Current
(red)
Voltage
(green)
-
Voltage
30º
Current
(a) No phase shift
(b) 30º phase shift
Power
+
-
Power
+
-
Current
Voltage
(c) 60º phase shift
60º
Current
90º
Voltage
(d) 90º phase shift
Fig. 9-3 Power in phase-shifted circuits. At 90º of
phase shift, the power is zero.
INDUCTIVE ONLY
RESISTIVE ONLY
CAPACITIVE ONLY
ALL 3 COMBINED
TRUE POWER
IS THE ACTUAL POWER USED BY THE CIRCUIT.
IT IS MEASURED WITH A WATTMETER.
APPARENT POWER
POWER IN A CIRCUIT WHEN VOLTAGE AND POWER ARE MEASURED SEPARATELY
IT IS CALCULATED IN UNITS OF VOLTAMPERE. (VA)
PTRUE = IVCOSØ
PAPPARENT =IV
POWER FACTOR
IS THE RATIO OF TRUE POWER/APPARENT POWER.
WHEN CURRENT AND VOLTAGE ARE IN PHASE THE POWER FACTOR = 1.
IF 90° OUT OF PHASE THE POWER FACTOR = 0.
POWER FACTOR OF A CIRCUIT CAN VARY BETWEEN O AND 1.
Power Factor (PF)
Power factor is defined as the ratio of true power (measured in watts) to
apparent power (measured in Volt Amps). It measures how effectively AC
power is being used by a device. The difference between true power and
apparent power is expressed as the power factor and results from the way true
power and apparent power are measured. Ideally we would like to have true
power and apparent power equal to one another, which would result in a PF of
1.00 or 100% effective power utilization.
AC Volts x AC Amps = VA (Volt Amp)
Purely Resistive AC Load: VA = Watts (same as DC circuits)
Inductive/Reactive AC Load: VA x PF = Watts
AC Volts x AC Amps x PF = Watts
A Power Factor of 0.75, means that an
installation is using 75% of the power being
supplied to it.
Aerovox manufactures both single and
three-phase power factor correction
capacitors up to 4,800 VAC
3 PHASE 277 V/480V, 4 WIRE WYE SYSTEM
LINE 1
277 V
PHASE 1
277 V
480 V
NEUTRAL
PHASE 3
277 V
PHASE 2
277 V
277 V
TO 3 PHASE
LOADS
480 V
LINE 2
GROUND
277 V
480 V
LINE 3
UNDER LOAD:LINE AND PHASE CURRENTS ARE NOT EQUAL.
SINCE 2 PHASE VOLTAGES ARE SEPARATED BY 120º , THEY CANNOT BE ADDED TOGETHER
ILINE = 1.732IPHASE
VLINE = 1.732VPHASE
VLINE2 = 1.732(277V) =480 V
SINGLE PHASE 277 V ARE CONNECTED BETWEEN THE NEUTRAL AND ANY LINE.
SINGLE PHASE480 V CIRCUITS ARE CONNECTED BETWEEN ANY 2 OF THE 3 LINES.
3 PHASE 480 V ARE CONNECTED ACROSS 3LINES.
RESISTIVE LOAD
IF WE ADD A REACTIVE ELEMENT (CAPACITOR OR INDUCTOR)
TO THIS CIRCUIT, THE PF WOULD BE REDUCED.
METER USED TO MEASURE 3 PHASE POWER FACTOR