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RMS & Power Factor Measurements Power factor analysis is used in many applications. Some example applications are measuring the efficiency of delivering power to a large AC motor and measuring the efficiency of delivering power to a switching power supply. Power factor is defined as the ratio between actual power and apparent power. Actual power refers to the power actually delivered to a load. Actual power is obtained by averaging the product of voltage and current waveforms over one cycle of the source. Apparent power is defined as Vrms x Irms, where V is the voltage across a load and I is the current flowing to the load. By obtaining average power, Vrms, and Irms power factor can be easily calculated. All electrical loads draw some type of current in response to applied voltage. The most simple being the load that acts like a resistor. This type of device simply draws current in a linear fashion. In this case conventional meters measure RMS values appropriately. However, any device that draws current in a non-linear or non-sinusoidal fashion, such as a switching power supply, can trick the conventional meter. A conventional volt meter simply calculates the RMS value as A x 0.7071, where A is the peak voltage. Most conventional volt meters assume the input is sinusoidal and may introduce an error if the waveform is distorted or non-linear. Astro-Med instruments calculate true RMS by sampling the waveform and using digital signal processing. In addition, they can capture the original current and voltage waveforms and convert them for use with spreadsheets that simplify the calculation of power factor. The goal of this experiment was to evaluate the performance of Astro-Med instruments in making power factor measurements. Power factor measurements were carried out on five different devices, a resistive load, an Astro-Med Dash IV, an Astro-Med MT95K2, a drill, and an AC induction motor. In order to calculate the power factor, RMS voltage and current values had to be measured. In each case an Astro-Med AstroDAQ2 was used to measure RMS voltages, RMS currents, and to capture load voltage and current waveforms. Three methods were used to measure current, a shunt resistor, a current gun with one winding, and a current gun with two windings. A conventional meter was also used to measure RMS voltages and currents in order to compare them with AstroDAQ2 values. In the case of the resistive load the RMS current value measured by the conventional meter was found to be 1.52A and the RMS current value measured by the AstroDAQ2 was found to be 1.53A. These values are very close because a resistive load draws current in a linear fashion. In the case of the Dash IV the RMS current value measured by the conventional meter was found to be .36A and the RMS current value measured by the AstroDAQ2 was found to be .57A. There is a discrepancy due to the fact that a Dash IV has a switching power supply. Only the AstroDAQ2 with special digital signal processing can measure a non-linear signal accurately. The MT95K2 and the drill had similar results. They too, as with many electric devices, draw current in a non-linear fashion. Equipment List
Procedure for Calculating Power Factor Step 1: Device Setup. To measure the current into the Unit Under Test use a shunt resistor with very low resistance such as .05 ohm. The voltage across the shunt resistor can be converted into current by simply multiplying it by 1/Rshunt. Voltage should be measured across the load so that the shunt voltage is not included. Step 2: Data Acquisition Setup. Install a VO4 module in an AstroDAQ2. Set the range on channel 1 to ±200V. To make current measurements multiply the shunt voltage by 1/Rshunt. This can be done by using user scaling. For example, if Rshunt = .05ohm the scale factor should be 20. Set the scale factor on channel 2 to 20 and the offset to 0. Set the range on channel 2 to ±10 A or the appropriate range. Connect the probes for channel 1 across the load making sure not to include the shunt voltage. Connect the probes for channel 2 across the shunt resistor. Set the AstroDAQ2 sample rate to 5 KHz and the capture size to 1 Ksamples. Step 3: Data Acquisition. The three values needed to calculate power factor are RMS voltage, RMS current, and average power. Turn on RMS mode for channel one and channel two. Power up the unit under test. Note RMS voltage and RMS current readings. Turn off RMS mode. Perform data capture. Step 4: Data Conversion. Review record using AstroLINK Record Review. Zoom in on one cycle of the voltage and current waveforms by highlighting one cycle and clicking the zoom button. Make sure only one cycle is highlighted. If more or less is highlighted the accuracy of the calculation may be compromised. Convert the data by saving it into a spreadsheet such as Microsoft Excel. This is done by clicking the WinSave button on the review screen. When the WinSave dialog box appears check Original, Screen Only, and the appropriate file type, then hit OK. Step 5: Average Power Computation. The average power equation is Step 6: Power Factor Computation. The power factor is the average power divided by the apparent power. The apparent power is Vrms • Irms Test Results Three Independent tests
RMS Meter Comparison
Power Factor Measurements
Current Measurement Device Comparison
Note: RMS current and RMS voltage measurements for certain units under test vary between tests due to different operating conditions. Calculations RMS Voltage: There are two ways to find the RMS voltage. The first way is to simply read it off of AstroLINK is meter. The other way is to compute this equation.
RMS Current: There are two ways to find the RMS Current. The first way is to simply read it off of AstroLINK's meter. The other way is to compute this equation.
Apparent Power: Papp = Vrms • Irms Average Power: Average power can be easily calculated using a spreadsheet
Power Factor: PF = Pavg/Papp Linear Resistive Load Example
This is an example of the load voltage and load current waveforms for a resistive load. The resistive load consists of 3-25oh, resistors in series(75ohm total).The voltage and current signals are in phase and both are sinusoidal. The AC input signal is slightly distorted. This is due to poor AC quality and is explained later. With this type of load a conventional meter is adequate. If the AC input signal were more distorted a conventional meter would not be accurate enough. However, the AstroDAQ2 always gives an accurate RMS measurement because it samples the data and computes the true RMS value on the fly while taking into account any distortions. Non-Linear Switching Power Supply Example
This is an example of the load voltage and load current waveforms for a device with a switching power supply. The load used was an MT95K2. The current waveform is a non-linear signal. Ergo, conventional meters will not measure RMS current properly. Subsequently, they will not measure power factor correctly. The AstroDAQ2 gives an accurate RMS measurement because it samples the data and computes the true RMS value on the fly while taking into account any distortions. Linear Inductive Load Example
This is an example of the load voltage and load current waveforms for an inductive load. The load used was a 3/4 horse power single phase induction motor. The voltage and current signals are out of phase and both are sinusoidal. The AC input signal is slightly distorted. This is due to poor AC quality and is explained later. With this type of load a conventional current meter or power factor meter will work fine except for the inaccuracy due to distortion. However, the AstroDAQ2 gives a more accurate RMS measurement. The power factor of this motor was found using a commercial power factor meter and an AstroDAQ2. The power factor value using the AstroDAQ2 was found to be .3 and the value using the commercial power factor meter was found to be .3. When the commercial power factor meter was used on the switching power supplies and the power drill it failed. This shows that some commercial power factor meters can only be used to accurately measure the power factor of a purely sinusoidal load. An AstroDAQ2 can measure the power factor of any load. Astro-Med Power Quality Analysis Voltage supplied to Astro-Med.
The voltage waveform is slightly distorted. Waveforms were acquired at 4 other locations throughout the Astro-Med plant and each location had distorted waveforms similar to the above waveform. Voltage supplied to another location in Exeter, RI.
The voltage waveform is not distorted. This test was done at another location and the waveform was undistorted.
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. Using a spreadsheet compute the product of the voltage and current for each sample. These values are the instantaneous power. Sum the instantaneous power values. Then divide this sum by the number of samples in the cycle. This value is the true average power. 
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