# Power Analysers: True RMS Readings 2013-11-08

Power measurements are becoming more and more important! Today, a big effort is being made to reduce power consumption; for that purpose, accurate power analysis and measurements are required. In order to be able to perform these measurements, there are specific instruments called Power Analysers.

A Power Analyser is a multifunction instrument which can measure single and three-phase electrical circuits. Most of them can measure:

- Instantaneous Power (W)

- Instantaneous Volt – Amperes (VA)

- Reactive Power Volt – Amperes (VAR)

- Power Factor / cosφ

- Harmonic Distortion

- Average Power

- Maximum Power

- RMS Voltage

- Peak Voltage

- RMS Current

- Phase Angle

- Crest Factor

- Frequency

- Energy (Wh)

These measurements are used in order to determine how electrical power is consumed, to calculate loads and costs and generally to evaluate the use of electrical energy. Energy analysers are used in several applications such as air conditioning and heating systems, power plants, motor loads, industrial applications and R&D purposes.

Since the measurements of a power analyzer are based on AC voltage and current measurement, especially RMS (Root Mean Square) values, it is important to find out why a power analyzer should take True RMS readings!

The RMS value comes from the mathematical formula that calculates the "effective" value (or heating value) of any AC wave shape. In other words the ACRMS value is equivalentto the DC heating value of a particular waveform. For example, if a resistive load produces 20 kW of heat at 240 V AC RMS, then we would get the same amount of heat if we applied 240 V DC instead of AC. Before proceeding, it would be helpful to define also two other terms which are going to be used below: Average value and Peak value:

The average value of a periodic waveform whether it is a sine wave, square wave or triangular is defined as the quotient of the area under the waveform with respect to time. In other words, it results from the averaging of all the instantaneous values along time axis with time being one full period, (T). The average value of a symmetrical alternating quantity, such as a sine wave, is the average value measured over only half a cycle since over a complete cycle the average value is zero.

The Peak value is the highest value of a waveform.

There are Power Analyzers which do not have a True RMS circuitry and use other methods to find the RMS value. These methods are based on the fact the RMS value can be calculated from the following formulas:

RMS value = 1,1 x Average Value

RMS value = 0,707 x Peak Value

These analysers actually measure the Peak Value (Peak-responding analysers) or the average value (average-responding analysers) and use these measurements to calculate the RMS value. In a world where every waveform would be a pure sine wave, this calculation would be enough to provide the required accuracy! In true life however, where other waveforms are used, or the loads contain power semiconductors,rectifiers or SCRs which result to non-linear loads, these methods lead to reading errors of up to 40% depending on the wave form! Since Electrical Power is calculated by multiplying the RMS voltage value to the RMS current value, imagine the error which would result in this case!

On the other hand, there are Power Analysers which use modern technology to directly measure RMS values instead of deriving them from other measurements. These instruments are called True RMS Power Analysers and are considered to be of a higher reliability and accuracy.

In real life, where not all loads are purely resistive and not all waveforms are pure sine waves, it is important to check if the Power Analyser we are using carries the reference “True RMS” on its front panel. If not, it could be possible that our measurements do not exactly correspond to the true values!

Barry Atkins
• nutech, trancient, fezder and 1 other person
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