Using modular digitisers for power measurements
Keywords:power measurements? Modular digitisers? oscilloscope? probes? digitiser?
Basic power measurements
Instantaneous power is calculated as the product of applied voltage and current. Real power (P) is the average or mean value of the instantaneous power measured in Watts. Circuits containing reactive elements (inductors or capacitors) can store energy and reverse power flow so that power flows from the load back to source. This is reactive power (R), measured in units of Volt-Amps Reactive or VAR. The vector sum of the real and reactive power is called total or apparent power (figure 1).
Figure 1: Vector diagram of the power components. |
Apparent power (S) can be computed as the product of the effective or rms voltage and effective or rms current. The units of apparent power are Volt-Amps (VA). The angle () enclosed by the real and apparent power vectors represents the phase difference between the current and voltage waveforms. The cosine of that angle, the ratio of real power and the apparent power is called the Power Factor (pf): pf = Cos() = P/S
If the device is purely resistive, then the current and voltage waveforms are in phase, the apparent and real power are equal, and the power factor equals one. As the reactive component increases, the power factor decreases.
Measuring line voltage
Figure 8: Computation of total power using a tow wattmeter method requiring only 4 digitiser channels along with two differential and two current probes.
Voltage measurements require the use of probes. Conventional oscilloscope, high-impedance probes can be used with a digitiser. The ability to scale vertical voltage data to account for the probes is very useful. Since most power measurements require line (mains) voltage measurements, it is best to make these measurements differentially in order to avoid grounding issues associated with single-ended probes. The digitiser should be able to accept two probe inputs and compute the difference. Alternatively, the voltage on the hot and neutral lines can be acquired separately and subtracted using waveform calculations. You could also use a differential probe.Measuring line current
The most convenient method of making current measurements is to use an appropriate current probe. Make sure that any current probe you use has controls separate from the measuring instrument. The output of the current probe can be applied to a digitiser channel with appropriate scaling to display signals from the probe in units of current.
Choosing a digitiser
Most line frequency measurements are made with fundamental frequencies of 50 to 400Hz, so the bandwidth requirements of a digitiser are not very great. If you want to perform conducted emission testing, then having the ability to accommodate up to the 40th harmonic of the power fundamental without significant loss is useful. This would place the bandwidth requirement at about 20kHz or greater.
The digitiser should have sufficient amplitude resolution to render the higher order harmonics of the power line, 12 to 16 bits will suffice.
The number of channels depends on whether single end or differential measurements are intended. Differential measurements combine two channels for each measurement. For a single-phase line measurement ,four input channels will yield two differential channels. For three phase measurements on each phase, six or greater channels are required. For example, three differential voltage channels and three single-ended current channels would require nine channels. Since most digitisers offer one through sixteen channels in a binary progression (1/2/4/8/16) you should select the next higher number of channels to accomplish the measurement task.
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