RMS versus Mean: The Importance of True RMS Monitoring

Monitoring the current draw of the IT equipment in data centres is becoming ever more important in the quest to reduce carbon emissions and energy costs. A variety of devices are available to perform that monitoring, and these typically provide either True RMS readings or Mean readings. This blog provides an overview of both methods and explores their validity in relation to monitoring the power drawn by servers, PCs and other IT equipment.

RMS, Mean and ‘What’s the Difference?’

In an electric circuit, the current in the load and voltage across it, defines the power delivered to, or consumed by the load. In a circuit where direct voltage or direct current (DC) is applied, the power then applied to the load is simply the product of the measured voltage and current at the load. However, DC power is rarely used to provide power to domestic and industrial loads since the power distribution networks work using alternating current (AC).

In measuring the AC quantities (voltages and currents), the same “scale” is used as that which would apply if the same voltage or current applied to the load were DC to deliver the same circuit power delivered to the load. This scale is called the RMS value (Root of the Means Squared). So, for a fixed load, 240V AC delivers the same power as 240V DC, and likewise for the current. In other words, the RMS value of an alternating voltage or current is exactly equivalent in its effect on the circuit as the same value of direct voltage or current. Thus a 60 Watt light bulb will have the same brightness and dissipate the same amount of heat regardless of whether it is supplied with 240V AC or 240V DC.

So, why is an RMS measurement necessary? It is necessary because an alternating current or voltage from the mains power supply is constantly varying in relation to time in a sinusoidal manner or as a sine wave, whereas a direct current or voltage is time invariant or constant. In general, for a RMS measurement, this variation can be anything as long as it is in a cycle, ie. that it repeats itself; it does not have to be a sinewave, it can be any repetitive wave shape that occurs within a set period of time. The RMS value yields the equivalent effect on an alternating current or voltage circuit by the same value of direct voltage or current for the defined period of time, thus:-

TrueRMSImage1

Is equivalent to –

TrueRMSImage2

…and

TrueRMSImage3

Is equivalent to –

TrueRMSImage4

Fig. 1

It is important at this point to understand that both the arithmetic mean and average of a sinewave is actually zero. This quantity is clearly wrong to describe the effect on a circuit of a sinewave voltage or current as they too would be zero, meaning that the average or mean power delivered to the load is also zero! The correct quantity to use in determining the real power delivered to a load is always the RMS or True RMS (as it is sometimes referred to). For any given load, the real power delivered to it is either the product of the current squared and the load resistance, or the voltage squared divided by the load resistance. Hence the RMS quantity takes the square root of the mean of the sum of the instantaneous current or voltages squared over a complete cycle. The net effect is to eliminate all negative values to yield a positive result. This can also be done on a DC or constant value of voltage or current – which would of course yield exactly the same value of the constant quantity, and therefore RMS value = DC value as already stated.

The shape of the current or voltage waveform will determine what its RMS value is because of the squaring of the instantaneous voltage or current.

Many loads produce modified or distorted sinewave shapes for the current despite a clean applied sinewave of voltage. This distortion can adversely affect the reading of many types of ammeters. The reason for this is that many are fundamentally not true RMS reading instruments (hence the term). These instruments are generally cheaper because they do not involve the mathematics of doing the RMS calculation. Instead they rectify (ie. remove the negative values of) the waveform and simply take the average of the rectified result. This is generally the mean value as it is averaged with a smoothing circuit to give a steady reading. If this type of voltmeter or ammeter is to be used only in a circuit where pure or undistorted sinewaves are present, then the mean value is scaled to the RMS value giving a pseudo RMS reading. However, this pseudo reading can only be accurate while the sinewave voltage or current remains undistorted.

The degree of distortion and hence the deviation or discrepancy between a True RMS reading ammeter and a mean (or pseudo RMS) reading ammeter will depend on the amount of the current waveform distortion in relation to a true un-distorted sinewave. Most loads that consist mainly of electrical resistance only, will not distort the waveform. Those that have inductance (eg. motors ) can distort to varying degrees depending on the magnetic linearity and how close to saturation they operate. Loads that have switch mode power supplies (eg. servers, PCs, printers, fax machines, etc.) produce the most distortion and will yield the largest discrepancy between mean and true RMS ammeter readings.

Figure 2 shows an example of the current waveform produced by a load that contains a switch mode power supply (eg. a PC or server). Generally, the true RMS value will be higher than the rectified mean, although this will depend somewhat on the amount and type of waveform distortion.

TrueRMSImage5

Fig. 2

The non sinewave form is often referred to as harmonic distortion or harmonic content. This is because the distortion can be represented by the addition of other frequencies that are harmonics or odd or even multiples of the fundamental mains frequency, eg. 100, 200 are the even 2nd and 4th harmonics and 150, 250 are the 3rd and 5th harmonics. The actual waveform shape is determined by the phase relationship and amplitude of these harmonics. For this reason, the power factor of the load is also associated with harmonic content and is also related to the RMS value of the circuit power. This is particularly true for switch-mode power supplies which, because of their widespread use, now incorporate special techniques to ensure a good power factor.

Summary

Although there may be initial cost benefits of using current monitoring devices that only provide mean readings, there are extremely strong arguments to say that True RMS monitoring devices and sensors should be the preferred choice in data centre environments due to the prevalence of servers and other distorted waveform loads. The less the waveform distortion of a particular load, the more likely we are to see similar readings between True RMS monitoring devices and Mean monitoring devices. Unfortunately though, switch mode power supplies used in servers and other IT equipment do produce a high degree of distortion: So the argument for the employment of True RMS measurement devices to obtain more accurate readings becomes stronger.

This argument is further endorsed by the fact that electricity meters used to provide power billing information are True RMS meters.


True RMS Monitoring Power Sensors from Jacarta:

PowerZook

intelliAmp

IT Power Audit Kit

Call: +44 (0) 1672 511125 •  Email: [email protected]
Jacarta Ltd, Wagon Yard, London Road, Marlborough, Wiltshire, SN8 1LH United Kingdom

ISO9001 Registered Inc. in England. Company No. 3426367 VAT No. GB 663 4687 04


© Jacarta 2020 | Terms & Conditions | Privacy Policy