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1. The Theory of Power Measurement.

The momentaneous Power Consumption for any Analog Continuous Periodic
Signal with a period of T, a voltage V(t) and a current I(t) is
calculated from the definition: $PT = {\frac 1 T} {\int_0^T (V(t) * I(t))dt}$

In the discrete world as implemented by the micPowerÛ Digital Sampled
Systems this formula becomes: $PT = {\frac 1 T} {\sum_{n=0}^{n=n+(T*Fs)} (V(n) * I(n))}$

Fs = sampling frequency, V(n) = voltage sample and I(n) = current
sample. The RMS (Root Mean Square) Current and Voltage is calculated as
follows:

$ITrms = {\sqrt {\frac 1 T {\sum_{n=0}^{n+(T*Fs)} (In)^2}}} {... and ...}UTrms = {\sqrt {\frac 1 T \sum_{n=0}^{n+(T*Fs)} (Un)^2}}$

Apparent Power is defined as: $VA = UTrms * ITrms$

The Power Factor for all waveforms is defined as this: $PF = \frac {PT} {VA}$

The Power Factor is equal to cosphi ONLY for sinusoidal shaped voltages
and currents. Competitors that advertises they do power measurement
from the formula like this: SQRT 3 * U * I * cosphi do NOT measure
power correctly, when they measure power before or after a variable
Frequency Inverter. They will only measure power correct, when the AC
Motor is connected directly to the main supply and NOT even through a
soft starter. The micPowerÛ family measure Power correct as shown from
the formulas above. The micPowerÛ family of Load Controller and Power
Monitors measures Power for Frequencies up to 30 kHz and any shape of
voltage and current curves. The micPowerÛ family measures Power correct
also when connected after a Variable Frequency Inverter.

2. The Current Measurement Transducer.

Until today Micro Power has designed and implemented Power Measurement
devices with three different type of sensors for Current Sensing:
Current Transformers, Hall Sensors and Shunt Resistors. The old fashion
typical Load Controller normally uses a Current Transformer for the
measurement. The Current Transformer is a reasonable accurate Current
Sensor. The CT includes an inductor and a metal or ferrite coil and for
this reason it is not a linear component over a larger frequency range.
This is fine, when it is used directly on the Main Supply of 50 or 60
Hz, but when it is used to measure Power after a Variable Frequency
Inverter the absolute accuracy is decreasing. Still the Current
Transformer is a very robust and low-cost passive component and for the
most applications considered good enough to implement the Load
Monitoring task. Current Transformers are very often used for Load
Control and Monitoring of symmetric loads (3-Phase AC Motors) in a
Single-Phase measurement configuration. A symmetric load is an
application where it is reasonable to assume that the load in each
phase is the same. This makes it possible to measure the load (Power)
in a single phase and multiply by three to get the full load. Micro
Power implements a true 3-phase extremely accurate device that is often
priced below competitor single-phase devices. Micro Power is bringing
unusual high accuracy devices to the Load Monitoring market. A truly
Asymmetric Measurement will be more accurate than a Single-Phase
Symmetric Measurement device, while the 3-phases are never exactly the
same.

The Hall Sensor is an active component that senses a magnetic field
proportional to the Current Flow and is more accurate and more linear
than the Current Transformer. The Hall Sensor has got a large
Measurement Range and a single Hall Sensor may be able to cover a
Current Range from below 1 Amp. to more than 100 amp. This would
usually need two cascade coupled Current Transformers. But Hall Sensors
are typically more expensive than Current Transformers and as they are
an active component, they need a DC-Power Supply to work. Both the Hall
Sensor and the Current Transformer sense the Current without breaking
the wire. This may be an advantage in some applications, while it is
not always easy to break and reconnect wires that carries huge loads of
Current (Amps).
The Shunt Sensor is a precision low-resistance resistor where the
current flows through. The voltage drop across the resistor is a
measure for the current that flows through the resistor (Ohms law).
Shunt Resistors are linear over a large frequency range and the most
accurate Current Sensor available. While the current must flow through
the Shunt Sensor the wire must be cut and connected to the transducer
input and output terminals. The Shunt Sensor is so accurate that it can
be used for extremely high precision current sensing. The actual
precision is often based on the accuracy of the Shunt Resistor itself,
which is typically in the range of 0.1% to 1%.

The 3 phase Voltages are always measured by a Resistor Ladder, which is
comparable to the Shunt Measurement accuracy.

References

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