** Understanding RMS values **

From Roy Lewallen

The RMS value of power is not the equivalent heating power and, in fact, it doesn’t represent any useful physical quantity.

I believe Mr. Roy Lewallen took an extreme position. In order to address the issue properly, we need to re-examine the whole concept of rms value carefully.

Let me start with the top slide. In this slide, I show the sinusoidal Voltage curve on top. I show the sinusoidal Current curve in the middle. I separated this middle curve into section X where the Voltage and Current are in Phase. There is a section Y where they are out of phase.

The last curve is the product of the instantaneous voltage values multiplied by the instantaneous current values. Note that in section X, the product (area) will always be positive. (Negative voltage time negative current will become positive number).

In section Y, the product will sometime produce positive value and sometimes negative value. Please examine the P curve in section Y carefully to confirm it.

**The question is – if the correct area can be obtained by flipping the negative area, why should the Industry introduce an RMS value?**The answer lies in slide 2 and slide 3 from

http://en.wikipedia.org/wiki/Root_mean_square.

In power measurements, we can still use the concept of Instantaneous P = Instantaneous V x Instantaneous I. Instantaneous V can still be represented by Instantaneous I x R where R is a fixed resistance. Thus the Instantaneous P = R * I * I.

The mathematics shown on slide 3 shows the usefulness of the RMS value in calculating Power. The negative sign is automatically guaranteed to be positive with the square function. Any integration will involve positive numbers only.

The rms Power by itself is not useful in providing an accurate power value. However, if there are a number of prototypes to be ranked, this rms Power value will provide a good ranking order. This can be confirmed with a number of prototypes (say 5) with different true COP > 1 values (obtained by the exact area integration method). These prototypes are again ranked with the (Output rms Power value divided by Input rms Power value). The ranking order will be the same.

Thus the Tseung FLEET Comparison Index has very solid scientific backing and must not be dismissed because someone does not understand or care to understand it.

To summarize,

1. If the Instantaneous Power Curve is all positive, the Poynt99 method of using a Mean Power Value for calculation is 100% correct. The result will be the same as with the exact area integration method.

2. If the Instantaneous Power Curve has positive and negative areas, the Poynt99 method MUST not be used.

3. The RMS method is useful because it automatically changes all numbers into positive for integration. And the value is directly relevant for Power Calculation because the square of I or V is involved.

4. The rms Power value is useful in providing a ranking order for different prototype. However, if the more exact area integration results are available, such results should be used.

More to come on Pulsing waveforms, importance of scope sampling rates and difference between DC and AC power concepts.