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 micPower® 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 cosϕ ONLY for sinusoidal shaped voltages and currents. Competitors that advertises they do power measurement from the formula like this: √ 3 * U * I * cosϕ 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 micPower® family measure Power correct as shown from the formulas above. The micPower® family of Load Controller and Power Monitors measures Power for Frequencies up to 30 kHz and any shape of voltage and current curves. The micPower® 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.