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# Power Meter Tutorials

- Calibration
- Measurement
- Background

## Measurement

Theory of Electric Power

## What is Electric Power

- Definition: Power per 1 hour by using Electric Energy
- Image: Value of Energy to accomplish a Job such as Moving, Lighting and Heating

- Definition: A Work Load of Electric Energy

- At the case of actual DC driven equipment, input level of both DC voltage and DC current is not stable. Therefore, power measuring instrument is required to measure not only DC signal but AC input (transient signal).

## AC power at the condition of sine wave

At the condition of sinusoidal inputs, AC Power is calculated by three parameters such as Voltage, Current and Phase Angle between those waveforms. The phase angle is decided theoretically depending on impedance of the load. Also, input frequency influences the error of power meter .

Impedance of ideal load is classified as below

Impedance of ideal load is classified as below:

- Resistance (No phase difference between V&A)

- Reactance (Phase of current is delay)

- Capacitance (Phase of current is forward)

## Power Factor

Definition : Power ratio respected to inputted Apparent Power Relation among parameters of electric power(Single Phase)

Note: Power Factor Error

- Power Factor Error (Difference of delay of phase angle between voltage input circuit and current circuit)

- Total Error including Power Factor Error

Measuring Error of Power is calculated by summation of Voltage measuring error, Current measuring error and Phase angle error.

## Distorted input(waveform)

Crest Factor : Ratio of PEAK value respected to RMS value

Crest Factor of measuring instrument and inputted waveform

- Inputted waveform : Characteristic of the waveform (measured by a function power meter)
- Measuring instrument : Specification(allowable Crest Factor) of power meter at condition of displaying range rated value on the DISPLAY

If the specification of the power meter is CF=3, 2Arms*3=6Apeak distorted waveform is allowable to measure. So, if input is 0.2Arms(10% of the range), 6Apk/0.2Arms = 20 times is allowable to measure. In this case, CF is 20. /p>

## Power of distorted waveform

When voltage(also current) consists of DC component, fundamental component and many harmonic components, the waveform is expressed as below;

In this condition, Power of the distorted waveform is the sum of effective power of identical frequency components contained in Voltage and Current as below;

Therefore, if voltage and current waveforms and those frequency components are showed as below figure, Power is calculated by using limited frequency components of Current frequency range(narrower frequency range) . Narrower bandwidth is enough.

## RMS and True RMS

True RMS(RMS calculation) :AC voltage or AC current value which occurs same Power consumption as DC voltage/current value when it is inputted to pure resistance. For example, 1Vrms and 1Vdc can occurs same energy. The expression is as below.

RMS(Rectified Mean calculation) : Low cost measurement or calculation method to get same value as True RMS method at the condition of sinusoidal input. The expression is as below.

When sinusoidal is inputted, there is no difference of result between RMS and True RMS. However, if it is distorted waveform, calculation result is different. It is problem.

In Japan, JEMA(Japanese Electric Machinery Association) decided to use RMS(Rectified MEAN) calculation method to measure out put voltage of PWM type Inverter. Because the value is proportional to torque output of its driven motor. It is important for their specification.

## Measurement of Three Phase Power

Three Phase Electric Power can be calculated to sum of each power value by using separated three power meters.

Also, Theory of Brondel said that n-phase electric power can be measured by using n-1 units of power meters. Therefore, three phase power is measured two power meters. The method is called two power meters method and is popular in Japan.

- Three phase three wire system (measurement of 3 voltages, 3 currents)

- Three phase three wire system (measurement of 2 voltages, 2 currents)

Wrong wiring (It occurs frequently.)

Influences of high frequency common mode voltage of Inverter driven motor (It requires know-how to solve depending to the case.).

## Tractability of Power