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L3026.5
Drexel University
Electrical and Computer Engineering Dept.
Electrical Engineering Laboratory II, ECE L 302
C. O. Nwankpa
Measuring AC Electric Power
“This endless circulation of electric fluid may appear paradoxical, but it is no less true
and real, and you may feel it with your own hands.”
Alessandro Volta
Table of Contents
•
Educational Objective
•
Introduction
•
Theory
•
Steps
Educational Objective
The object of the experiment is to learn how to appreciate AC circuits by understanding
the main components as well as variables that are influenced by them. These variables are
AC voltages and currents. AC power will be shown to be the result of calculations
involving these variables.
Introduction
In order to fully understand AC circuits, a popular tool will be reintroduced.
This tool is
referred to as phasor diagrams.
Phasor diagrams describe timevarying quantities such as
voltages and currents using complex number representation:
V
V
θ
=
∠
V
I
I
=
∠
I
In this course we shall appreciate the use of these phasor notations as a powerful tool
used to define electric power.
In order to evaluate AC power, one needs to usually find the product of voltages and
currents, because by definition power is:
p
tv
ti
t
()
=
×
61
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As will be seen in the next section, various types of power exist and we will try to define
and differentiate them from one another.
Background Information
As you shall learn during this lab: there are various types of power.
Example of these
are: instantaneous, average, real, reactive, total, apparent, etc.
We shall analyze several
of these different types of power and attempt to clarify the differences between them.
a)
Instantaneous power
.
Consider a linear network which has steadystate currents and voltages, periodic
functions in time (both of period
T
), as inputs. The outputs will also be currents and
voltages which are also periodic functions in time.
Instantaneous power is defined as
below,
p
tv
ti
t
()
=
×
In this definition it is noted that instantaneous power is a function of time and also
periodic (but not necessarily of period
T
).
Note: whatever the fundamental period of
p(t)
is, let us denote this as
T
p
, T
must contain an integral number of periods of
T
p.
b)
Average power.
Consider the above definition of instantaneous power.
Two things stand out: (i)
The time varying nature of
p(t)
and (ii) the periodic nature of
T.
So to present
average power, there is a need to evaluate an average value of
p(t).
The averaging so
to say must be performed over a period of interest. The question now is over what
period?
T
p
or
T.
To answer this, look at the following relationship:
P
T
ptd
t
T
t
p
t
tT
p
t
==
++
∫∫
11
1
1
1
1
P
is average power.
From this we can see that it doesn’t matter whether or not we use
T
p
or
T
just as long as make the corresponding necessary changes in the limits of the
integral.
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This document was uploaded on 09/25/2011.
 Spring '09

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