OK. Here goes:
AC power (real power as opposed to volt-amps) flowing through a circuit
(single phase) is the product of the voltage phasor magnitude (the rms
value one would read with a meter), the current phasor magnitude, and
the power factor. The power factor is the cosine of the phase angle
between the above voltage and current phasors. This is valid for
sinusoidal voltage and currents but has problems if the voltage and/or
current contain harmonics.
Alternately, one can multiply the instantaneous current and voltage
values of the circuit and sum the result over one cycle (or several
cycles). This is (sort of) how a mechanical watt meter (or watt-hour
meter) works. The meter is a special kind of AC motor whose torque is
proportional to this product.
For a watt meter, this torque acts against a spring to move a pointer.
For a watt hour meter, this torque acts against a known drag to produce
a certain number of rotor revolutions per watt-hour. The disk
revolutions per watt hour is known as Kh and can be seen on the
nameplate of meters.
There are solid-state (analog and digital) methods of performing the
above multiplication instead of the electromechanical method. These
appear in most modern test equipment (where space and weight is at a
premium), calibration equipment and large scale metering (where the cost
of the precision circuitry can be absorbed).
For three phase systems, three 'elements' are used, one for each phase,
to perform the above multiplication. These 'elements' might be three
separate current/voltage winding sets in an electromechanical meter, or
three sets of calculations performed and summed in a uP.
If you work out the vector math (maths for all our UK readers), the
voltage phasors used in the above sum for any N-wire system can be a
phasor measured from the phase conductor to _any_ common reference point
in 'phasor space'. As long as the same reference point is used for all
VI products, the sums of all the power flows will equal the total power
flowing through the circuit at that point. By selecting this common
point to be one of the circuit conductors, one can eliminate one
metering 'element' and still get the total power. This is because the
voltage phasor from that reference point to itself is always zero, so
the product of that conductor's current and zero is ... zero.
For a two wire circuit, one line current and the voltage from that line
to the other is measured.
For a three phase, four wire circuit, if the neutral is used as the
reference, only the three phase currents are taken and multiplied by the
phase to neutral voltages. For a three phase, three wire circuit, one
phase is used as a metering common. Only the other two phase currents
and the phase to phase voltages are measured to meter the power flow.
Paul Hovnanian mailto: snipped-for-privacy@Hovnanian.com
I thought that those were for measuring the imaginary
power that make the difference between watts and vars.
Photovoltaic Resources Int'l
Tempe Arizona USA
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