**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.