Power measurement
Power measurement in AC circuits can be
quite a bit more complex than with DC circuits for the simple reason
that phase shift makes complicates the matter beyond multiplying voltage
by current figures obtained with meters. What is needed is an instrument
able to determine the product (multiplication) of instantaneous
voltage and current. Fortunately, the common electrodynamometer movement
with its stationary and moving coil does a fine job of this.
Three phase power measurement can be
accomplished using two dynamometer movements with a common shaft linking
the two moving coils together so that a single pointer registers power
on a meter movement scale. This, obviously, makes for a rather expensive
and complex movement mechanism, but it is a workable solution.
An ingenious method of deriving an
electronic power meter (one that generates an electric signal
representing power in the system rather than merely move a pointer) is
based on the Hall effect. The Hall effect is an unusual effect first
noticed by E. H. Hall in 1879, whereby a voltage is generated along the
width of a current-carrying conductor exposed to a perpendicular
magnetic field:
The voltage generated across the width of
the flat, rectangular conductor is directly proportional to both the
magnitude of the current through it and the strength of the magnetic
field. Mathematically, it is a product (multiplication) of these two
variables. The amount of "Hall Voltage" produced for any given set of
conditions also depends on the type of material used for the flat,
rectangular conductor. It has been found that specially prepared
"semiconductor" materials produce a greater Hall voltage than do metals,
and so modern Hall Effect devices are made of these.
It makes sense then that if we were to
build a device using a Hall-effect sensor where the current through the
conductor was pushed by AC voltage from an external circuit and the
magnetic field was set up by a pair or wire coils energized by the
current of the AC power circuit, the Hall voltage would be in direct
proportion to the multiple of circuit current and voltage. Having no
mass to move (unlike an electromechanical movement), this device is able
to provide instantaneous power measurement:
Not only will the output voltage of the
Hall effect device be the representation of instantaneous power at any
point in time, but it will also be a DC signal! This is because the Hall
voltage polarity is dependent upon both the polarity of the
magnetic field and the direction of current through the conductor. If
both current direction and magnetic field polarity reverses -- as it
would ever half-cycle of the AC power -- the output voltage polarity
will stay the same.
If voltage and current in the power
circuit are 90o out of phase (a power factor of zero, meaning
no real power delivered to the load), the alternate peaks of Hall
device current and magnetic field will never coincide with each other:
when one is at its peak, the other will be zero. At those points in
time, the Hall output voltage will likewise be zero, being the product
(multiplication) of current and magnetic field strength. Between those
points in time, the Hall output voltage will fluctuate equally between
positive and negative, generating a signal corresponding to the
instantaneous absorption and release of power through the reactive load.
The net DC output voltage will be zero, indicating zero true power in
the circuit.
Any phase shift between voltage and
current in the power circuit less than 90o will result in a
Hall output voltage that oscillates between positive and negative, but
spends more time positive than negative. Consequently there will be a
net DC output voltage. Conditioned through a low-pass filter circuit,
this net DC voltage can be separated from the AC mixed with it, the
final output signal registered on a sensitive DC meter movement.
Often it is useful to have a meter to
totalize power usage over a period of time rather than instantaneously.
The output of such a meter can be set in units of Joules, or total
energy consumed, since power is a measure of work being done
per unit time. Or, more commonly, the output of the meter can be set
in units of Watt-Hours.
Mechanical means for measuring Watt-Hours
are usually centered around the concept of the motor: build an AC motor
that spins at a rate of speed proportional to the instantaneous power in
a circuit, then have that motor turn an "odometer" style counting
mechanism to keep a running total of energy consumed. The "motor" used
in these meters has a rotor made of a thin aluminum disk, with the
rotating magnetic field established by sets of coils energized by line
voltage and load current so that the rotational speed of the disk is
dependent on both voltage and current.
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