Yokogawa hopes that its Power meters contribute to a world with cleaner and more efficient energy use. The below tutorial intends to help with power measurement.
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:
Definition : Power ratio respected to inputted Apparent Power Relation among parameters of electric power(Single Phase)
Note: Power Factor Error
Measuring Error of Power is calculated by summation of Voltage measuring error, Current measuring error and Phase angle error.
Crest Factor : Ratio of PEAK value respected to RMS value
Crest Factor of measuring instrument and inputted waveform
For example : Condition - 2Arms range setting and displaying 2Arms (range rated value)
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.
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.
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.
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.
Switching Mode Power Supply is adopted to almost Household Appliances and Office Automation Equipment
The inputted current waveform is distorted like pulse wave and also voltage waveform is distorted same point as current. It includes so much harmonic components because of circuit design of capacitor input style.
Requirements for Power Meter;
Inverter Driven Motor
Type of Inverter : PWM is main method and PAM becomes popular
PWM(Pulse Width Modulation) : Revolution speed of motor is controlled by using change of pulse width of voltage waveform. And there are two types of method in PWM. One is Sinusoidal PWM and another is Square-wave PWM. The Sinusoidal or Square- mean current waveform of motor input.
PAM(Pulse Amplitude Modulation) : Revolution speed is controlled by amplitude of voltage. And the waveform both voltage and current are square. Therefore, frequency bandwidth of measuring instrument for current is required higher than PWM type inverter.
Requirements for Power Meter;
Inverter for high frequency fluorescent lamp
In general, the waveform is a kind of triangle or sinusoidal. And the fundamental frequency is below 100kHz. Also envelope is twice of commercial frequency.
Requirements for Power Meter;
Measuring method of fluctuating Electric Power (for example : Copying machine)
Requirement of Power Meter ;
Inductive Type Wh-meters, which are based upon the principle of mechanically averaging instantaneous power measure electrical energy consumed in a home for billing purposes. It is guaranteed only commercial frequencies 50/60Hz.
1: current coil 2: Short ring
3: Movable disk 4: Phase adjusting coil
5: magnetic shunt steel 6: manganin resistor
7: Secondary voltage coil 8: Voltage coil
Analog indicate type Power Meter
Principle : Repulsion of magnetic field caused by currents of both Fixed and Moving coils
Principle : Time Division Multiple analog circuit method Multiplication circuit
Principle : Digital filtering method of digital sampled data
We are afraid that we can not receive any standard calibration for small power(small current condition) below to 1W(at standby mode of electric equipment) in Japan at present time. Official Calibration Lab, JEMIC(Japanese Electric Machinery Inspection Corporation) can calibrate below to 10W only. Therefore, Yokogawa tried to show the guideline of accuracy for small power as blow. It consists of summation of Voltage error, Current error, Phase angle error and special calculation error of the power meter.
Also, all WT series can measure small current below to 2 or 3% of the range rated value as below graph. (It shows 500mA range of WT110.)
An example of linearilty error (0.5 A range)
Wiring technique for Reduction of Instrument Loss
We should pay an attention of reduction for the Instrument Loss in case of low power measurement below to approx. 0.5W. It causes of impedance of voltage input circuit. If the impedance is 1M ohm and 240 V input, it influences +0.058 W, more than 10% of target.
In such case, we should check the Wiring Method described in the Instruction Manual as below;
Recommended Wiring method for small current measurement
When current waveform is distorted and has big Crest Factor characteristic like condenser input type switching mode power supply, measuring current range should be selected properly. Otherwise, measured value is not accurate because peak part of the waveform is neglected or bigger current range is selected.
In such case, Energy Star Program decides to set proper range after measuring peak current and selecting suitable range.
|Object : TV, VTR, PC Printer, Copying Machine, FAX Machine|
When trend of power(or current) level is fluctuated as below figure, some power meters can not detect and measure small or rapid change of power(or current). Especially, it influences Watt-hour(Integration) measuring function. Therefore, we should check lower limit and response time of power meter before use it. Refrigerator, PC
Generally speaking, voltage and current waveforms of electric equipment are distorted recently. Therefore, broad measuring bandwidth is required.
In order to measure target within 0.1% accuracy, triangle waveform requires measuring bandwidth by 5 times to the fundamental frequency and 200 times or more for square waveform theoretically. Also measuring accuracy at the high frequency should be paid an attention.
However, frequency bandwidth depends on the bandwidth of lower frequency parameter as explained in this document. Therefore, frequency bandwidth is not first priority for distorted waveform.
Common Mode Voltage ; It locates between earth ground and target equipment and oscillated voltage is added to both Hi and Lo terminals commonly.
If impedance between Hi terminal loop(R1+Z1) and Lo terminal loop(R2+Z2) are different, current becomes different in the two loops and it occurs differential voltage between input terminals and causes measurement error.
|Voltage input terminals are shorted and connected one line of target. And current input terminals are opened and connected one line as right figure. The influence appears as measurement value according to below expressions.
Some equipment using intermittent operation(or control) method in order to reduce power consumption at standby mode requires long period measurement and averaging function till next oscillate as below figure.
Generally, power measuring instrument has settled measuring period and update cycle. Therefore, it should be set the longest period setting when it measure such equipment. And if it is not enough, averaging function should be set on.
It is important to set averaging period according to input waveform like PZ4000.
The WT2000 digital powermeter series has been designed with emphasis on basic performance (bandwidth, accuracy, response speed, and noise immunity) from the viewpoint of measurement of electrical quantities. The broad range of functions of these power analyzers enable them to be used in various fields of applications.