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Calculating Line-to-Line Voltages fromLine-to-Neutral Measurements with the NI9225

OverviewThis document explains how to calculate line-to-line values on a three phase 240V system from line to neutralmeasurements.

Assume you have a Y-connected 240Vac three-phase system as shown below in figure 1. The NI 9225 is connectedbetween each phase and neutral:

Figure 1. 240V 3-Phase System connected to NI 9225 300V AI module

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Meeting the NI 9225 Safety Specifications

Each channel in the NI 9225 will nominally have 240Vrms between the AI+ and AI- terminal. The NI 9225 is rated to300Vrms from channel to earth, so the measurement is within the safety specifications. Assuming a perfectly balancedsystem, each phase is separated by 120 degrees and the line-to-neutral voltage on each phase is the same. As long asthese two assumptions hold true, then the magnitude of the line to line voltage is 1.732 * Vp , where Vp is theline-to-neutral voltage. If the line-to-neutral voltage is 240Vrms, then the line-to-line voltage will be 416Vrms. The NI9225 is rated for 600V ch-ch isolation, so this voltage is within the safety specifications.

Measuring line-to-line Voltages - The Most General Case

The connection scheme shown above in figure 1 can be used to indirectly measure the line-to-line voltages on a

Y-connected systems. The line-to-line voltage is the vector sum of the line to neutral voltages. So, for example, if weknow Van, Vbn, and Vcn (defined as in the diagram below), we can find the line to line voltages as follows:

The following phasor diagram (diagram 1) will help visualize the phasor math required to convert from line-to-neutralvoltages to line-to-line voltages.

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Diagram 1. Line-to-line calculation phasors

We will start with an example showing how to measure Vab. As has been described above, the line-to-line voltage is thephasor sum of the line-to-neutral voltages, so

Nominally, each phase in a three phase system is spaced exactly 120 degrees apart. However, since our intent is toperform measurements in the system, we cannot assume it to be ideal. Because of this, instead of assuming 120 degreesof separation between phases, we will simply use #xx to denote the angle between two phases. Van as defined above haszero phase, and Vbn has a phase of #ab.

Breaking up Vbn into rectangular components results in the following:

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Subtracting the in-phase component of Vbn from Van:

From the rectangular components, we can calculate the magnitude of the line to line voltage:

To calculate the phase angle #ab, we now find the phase of the rectangular vector calculated above:

To illustrate the above, we assume the line-to-neutral voltages are 240V, and the phase to phase angle is 240V.

Vab = 415.7V (as referenced in the first paragraph of this document)

#ab = 30

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IMPORTANT: The assumption that the line-to-line voltage is sqrt(3) times the line-to-neutral voltage is only validwhen the magnitudes of the line-to-neutral voltages are all the same.

Measuring Line-to-Line Voltages When the Line-to-Line Separation is Exactly120 Degrees

If we can guarantee that the line-to-line phase is exactly 120 degrees, then the equations above can be somewhat

simplified. This may be the case when the power source is a generator with three rotor windings physically 120 degreesapart. If we again look at the example of finding Vab based on Van and Vbn, the magnitude and phase can be calculated asfollows:

This eliminates the need to calculate sine and cosine functions, although the square root and arctangent operations arestill needed.

Summary

The NI 9225 can be used to measure line-to-neutral voltages, which can in turn be used to calculate line to lineparameters. However, it must be noted that the relationship between line-to-neutral and line-to-line voltages involves

magnitude and phase, and both must be taken into account in order to obtain accurate line-to-line measurements. The

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phasor diagram below (diagram 2) shows the magnitude and phase relationship between all line-to-neutral andline-to-line voltages in the system.

Diagram 2. Magnitude and phase relationship of all voltages in system

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