Transcript DC Motors - Anne Arundel Community College

AC Power
Learning Objectives

Define real (active) power, reactive power and average
power.

Calculate the real and reactive power in AC series parallel
networks.

Graph the real and reactive power of purely resistive,
inductive, or capacitive loads in AC series parallel networks
as a function of time.

Determine when power is dissipated, stored, or released in
purely resistive, inductive, or capacitive loads in AC series
parallel networks.

Calculate the total real and total reactive power consumed in
AC series parallel networks.
DC Power

Power is the measure of work per unit time, or
joules/sec or watts.
2
V
2
P  VI  I R 
R
[w atts,W]
AC Power to a Resistive Load


In ac circuits, voltage and current are functions of time.
Power at a particular instant in time is given
Vm I m
p  vi  (Vm sin t )( I m sin t )  Vm I m sin t 
1  cos 2t 
2
2

This is called instantaneous power.
Average Power to a Resistive Load



p is always positive
All of the power delivered by the source is
absorbed by the load.
Average power P = VmIm / 2
Average Power to a Resistive Load

Using RMS values V and I
VRMS 
Vm
I RMS 
Im
2
2
rms value of voltage
rms value of current
Vm I m  Vm   I m 
P

 VRMS I RMS



2
 2  2 


(watts)
P is called real power or active power
because it is really dissipated by the load.
Active power is the average value of
instantaneous power.
Power to an Inductive Load

Consider the following circuit where
i = Im sin t .

Can we write an expression
instantaneous power or pL(t) ?
Power to an Inductive Load
i  I m sin  t
v  Vm sin(t  90)
p  vi  (Vm sin t  90 )( I m sin t )  Vm I m cos t sin t
Vm I m
 Vm   I m 

 sin 2t       sin 2t  VRMS I RMS sin 2t
2
 2  2 
Power to an Inductive Load



p is equally positive and negative.
All of the power delivered by the source is
returned.
Average power PL = 0 W
Reactive Power

Instantaneous power to an inductive load is
given by pL = VI sin 2 t

The product VI is called reactive power and
given the symbol QL.

The unit of QL is VAR (volt-amps reactive)
QL  VI
(VAR)
2
V
2
QL  I X L 
XL
(VAR)
Reactive Power
Reactive power is the portion of power
that flows into load and then back out.
 It contributes nothing to average power.
 The power that flows into and out of a pure
inductor is reactive power only.

Example Problem 1
For each circuit, determine real and reactive
power.
Power to a Capacitive Load

Consider the following circuit where
i = Im sin t .

Can we write an expression
instantaneous power or pC(t) ?
Power to a Capacitive Load
i  I m sin t
v  Vm sin(t  90)
p  vi  (Vm sin t  90 )( I m sin t )  Vm I m cos t sin t
Vm I m
 Vm  I m 

 sin 2t       sin 2t  VRMS I RMS sin 2t
2
 2  2 
Power to a Capacitive Load



p is equally positive and negative
All of the power delivered by the source is returned
(no power losses with a pure reactive load).
Average power PC = 0 W
Reactive Power

Instantaneous power to an capacitive load is
given by pL = -VI sin 2 t

The product VI is called reactive power and
given the symbol QC.

The unit of QC is VAR (volt-amps reactive)
QC  VI
(VAR)
2
V
QC  I X C 
(VAR)
XC
By convention, reactive power due to
capacitance is defined as negative.
2

Example Problem 2
Determine real and reactive power.
AC Power to a Resistive Load
AC Power to a Inductive Load
AC Power to a Capacitive Load
Power
Reactive components only store/discharge
power, they do not dissipate it.
 The power dissipated is entirely due to the
resistive component of impedance.

Total Power in AC Circuits


The total power real (PT) and reactive power
(QT) is simply the sum of the real and reactive
power for each individual circuit elements.
How elements are connected does not matter
for computation of total power.
P1
Q1
PT  P1  P2  P3 PP4
T
QT  Q1  Q2  Q3 QQT4
P2
Q2
P3
Q3
P4
Q4
Total Power in AC Circuits

Sometimes it is useful to redraw the circuit to
symbolically express the real and reactive power loads
Example Problem 3
For the RC circuit below, determine XC. If
frequency is 60 Hz, determine C.
Example Problem 4
For the RC circuit below, determine PT and QT.
If frequency is 60 Hz, determine C.